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7 Add Functions
 7.1 Functions Installed by Add
 7.2 Add Method
 7.3 InstallAdd Function
 7.4 Enhancing the method name record
 7.5 Install All Adds
 7.6 Prepare functions
 7.7 Available Add functions

  7.7-1 AddAdditionForMorphisms

  7.7-2 AddAdditiveGenerators

  7.7-3 AddAdditiveInverseForMorphisms

  7.7-4 AddAstrictionToCoimage

  7.7-5 AddAstrictionToCoimageWithGivenCoimageObject

  7.7-6 AddBasisOfExternalHom

  7.7-7 AddCanonicalIdentificationFromCoimageToImageObject

  7.7-8 AddCanonicalIdentificationFromImageObjectToCoimage

  7.7-9 AddCoastrictionToImage

  7.7-10 AddCoastrictionToImageWithGivenImageObject

  7.7-11 AddCoefficientsOfMorphismWithGivenBasisOfExternalHom

  7.7-12 AddCoequalizer

  7.7-13 AddCoequalizerFunctorial

  7.7-14 AddCoequalizerFunctorialWithGivenCoequalizers

  7.7-15 AddCoimageObject

  7.7-16 AddCoimageProjection

  7.7-17 AddCoimageProjectionWithGivenCoimageObject

  7.7-18 AddCokernelColift

  7.7-19 AddCokernelColiftWithGivenCokernelObject

  7.7-20 AddCokernelObject

  7.7-21 AddCokernelObjectFunctorial

  7.7-22 AddCokernelObjectFunctorialWithGivenCokernelObjects

  7.7-23 AddCokernelProjection

  7.7-24 AddCokernelProjectionWithGivenCokernelObject

  7.7-25 AddColift

  7.7-26 AddColiftAlongEpimorphism

  7.7-27 AddColiftOrFail

  7.7-28 AddComponentOfMorphismFromDirectSum

  7.7-29 AddComponentOfMorphismIntoDirectSum

  7.7-30 AddCoproduct

  7.7-31 AddCoproductFunctorial

  7.7-32 AddCoproductFunctorialWithGivenCoproducts

  7.7-33 AddDirectProduct

  7.7-34 AddDirectProductFunctorial

  7.7-35 AddDirectProductFunctorialWithGivenDirectProducts

  7.7-36 AddDirectSum

  7.7-37 AddDirectSumCodiagonalDifference

  7.7-38 AddDirectSumDiagonalDifference

  7.7-39 AddDirectSumFunctorial

  7.7-40 AddDirectSumFunctorialWithGivenDirectSums

  7.7-41 AddDirectSumProjectionInPushout

  7.7-42 AddDistinguishedObjectOfHomomorphismStructure

  7.7-43 AddEmbeddingOfEqualizer

  7.7-44 AddEmbeddingOfEqualizerWithGivenEqualizer

  7.7-45 AddEpimorphismFromSomeProjectiveObject

  7.7-46 AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject

  7.7-47 AddEqualizer

  7.7-48 AddEqualizerFunctorial

  7.7-49 AddEqualizerFunctorialWithGivenEqualizers

  7.7-50 AddFiberProduct

  7.7-51 AddFiberProductEmbeddingInDirectSum

  7.7-52 AddFiberProductFunctorial

  7.7-53 AddFiberProductFunctorialWithGivenFiberProducts

  7.7-54 AddHomologyObject

  7.7-55 AddHomologyObjectFunctorialWithGivenHomologyObjects

  7.7-56 AddHomomorphismStructureOnMorphisms

  7.7-57 AddHomomorphismStructureOnMorphismsWithGivenObjects

  7.7-58 AddHomomorphismStructureOnObjects

  7.7-59 AddHorizontalPostCompose

  7.7-60 AddHorizontalPreCompose

  7.7-61 AddIdentityMorphism

  7.7-62 AddIdentityTwoCell

  7.7-63 AddImageEmbedding

  7.7-64 AddImageEmbeddingWithGivenImageObject

  7.7-65 AddImageObject

  7.7-66 AddInitialObject

  7.7-67 AddInitialObjectFunctorial

  7.7-68 AddInitialObjectFunctorialWithGivenInitialObjects

  7.7-69 AddInjectionOfCofactorOfCoproduct

  7.7-70 AddInjectionOfCofactorOfCoproductWithGivenCoproduct

  7.7-71 AddInjectionOfCofactorOfDirectSum

  7.7-72 AddInjectionOfCofactorOfDirectSumWithGivenDirectSum

  7.7-73 AddInjectionOfCofactorOfPushout

  7.7-74 AddInjectionOfCofactorOfPushoutWithGivenPushout

  7.7-75 AddInjectiveColift

  7.7-76 AddInjectiveDimension

  7.7-77 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure

  7.7-78 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects

  7.7-79 AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism

  7.7-80 AddInverseForMorphisms

  7.7-81 AddInverseMorphismFromCoimageToImageWithGivenObjects

  7.7-82 AddIsAutomorphism

  7.7-83 AddIsBijectiveObject

  7.7-84 AddIsCodominating

  7.7-85 AddIsColiftable

  7.7-86 AddIsColiftableAlongEpimorphism

  7.7-87 AddIsCongruentForMorphisms

  7.7-88 AddIsDominating

  7.7-89 AddIsEndomorphism

  7.7-90 AddIsEpimorphism

  7.7-91 AddIsEqualAsFactorobjects

  7.7-92 AddIsEqualAsSubobjects

  7.7-93 AddIsEqualForCacheForMorphisms

  7.7-94 AddIsEqualForCacheForObjects

  7.7-95 AddIsEqualForMorphisms

  7.7-96 AddIsEqualForMorphismsOnMor

  7.7-97 AddIsEqualForObjects

  7.7-98 AddIsEqualToIdentityMorphism

  7.7-99 AddIsEqualToZeroMorphism

  7.7-100 AddIsHomSetInhabited

  7.7-101 AddIsIdempotent

  7.7-102 AddIsInitial

  7.7-103 AddIsInjective

  7.7-104 AddIsIsomorphism

  7.7-105 AddIsLiftable

  7.7-106 AddIsLiftableAlongMonomorphism

  7.7-107 AddIsMonomorphism

  7.7-108 AddIsOne

  7.7-109 AddIsProjective

  7.7-110 AddIsSplitEpimorphism

  7.7-111 AddIsSplitMonomorphism

  7.7-112 AddIsTerminal

  7.7-113 AddIsWellDefinedForMorphisms

  7.7-114 AddIsWellDefinedForObjects

  7.7-115 AddIsWellDefinedForTwoCells

  7.7-116 AddIsZeroForMorphisms

  7.7-117 AddIsZeroForObjects

  7.7-118 AddIsomorphismFromCoequalizerOfCoproductDiagramToPushout

  7.7-119 AddIsomorphismFromCoimageToCokernelOfKernel

  7.7-120 AddIsomorphismFromCokernelOfDiagonalDifferenceToPushout

  7.7-121 AddIsomorphismFromCokernelOfKernelToCoimage

  7.7-122 AddIsomorphismFromCoproductToDirectSum

  7.7-123 AddIsomorphismFromDirectProductToDirectSum

  7.7-124 AddIsomorphismFromDirectSumToCoproduct

  7.7-125 AddIsomorphismFromDirectSumToDirectProduct

  7.7-126 AddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct

  7.7-127 AddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram

  7.7-128 AddIsomorphismFromFiberProductToKernelOfDiagonalDifference

  7.7-129 AddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject

  7.7-130 AddIsomorphismFromImageObjectToKernelOfCokernel

  7.7-131 AddIsomorphismFromInitialObjectToZeroObject

  7.7-132 AddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject

  7.7-133 AddIsomorphismFromKernelOfCokernelToImageObject

  7.7-134 AddIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct

  7.7-135 AddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram

  7.7-136 AddIsomorphismFromPushoutToCokernelOfDiagonalDifference

  7.7-137 AddIsomorphismFromTerminalObjectToZeroObject

  7.7-138 AddIsomorphismFromZeroObjectToInitialObject

  7.7-139 AddIsomorphismFromZeroObjectToTerminalObject

  7.7-140 AddKernelEmbedding

  7.7-141 AddKernelEmbeddingWithGivenKernelObject

  7.7-142 AddKernelLift

  7.7-143 AddKernelLiftWithGivenKernelObject

  7.7-144 AddKernelObject

  7.7-145 AddKernelObjectFunctorial

  7.7-146 AddKernelObjectFunctorialWithGivenKernelObjects

  7.7-147 AddLift

  7.7-148 AddLiftAlongMonomorphism

  7.7-149 AddLiftOrFail

  7.7-150 AddMereExistenceOfSolutionOfLinearSystemInAbCategory

  7.7-151 AddMonomorphismIntoSomeInjectiveObject

  7.7-152 AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject

  7.7-153 AddMorphismBetweenDirectSums

  7.7-154 AddMorphismBetweenDirectSumsWithGivenDirectSums

  7.7-155 AddMorphismConstructor

  7.7-156 AddMorphismDatum

  7.7-157 AddMorphismFromCoimageToImageWithGivenObjects

  7.7-158 AddMorphismFromEqualizerToSink

  7.7-159 AddMorphismFromEqualizerToSinkWithGivenEqualizer

  7.7-160 AddMorphismFromFiberProductToSink

  7.7-161 AddMorphismFromFiberProductToSinkWithGivenFiberProduct

  7.7-162 AddMorphismFromKernelObjectToSink

  7.7-163 AddMorphismFromKernelObjectToSinkWithGivenKernelObject

  7.7-164 AddMorphismFromSourceToCoequalizer

  7.7-165 AddMorphismFromSourceToCoequalizerWithGivenCoequalizer

  7.7-166 AddMorphismFromSourceToCokernelObject

  7.7-167 AddMorphismFromSourceToCokernelObjectWithGivenCokernelObject

  7.7-168 AddMorphismFromSourceToPushout

  7.7-169 AddMorphismFromSourceToPushoutWithGivenPushout

  7.7-170 AddMultiplyWithElementOfCommutativeRingForMorphisms

  7.7-171 AddObjectConstructor

  7.7-172 AddObjectDatum

  7.7-173 AddPostCompose

  7.7-174 AddPostComposeList

  7.7-175 AddPreCompose

  7.7-176 AddPreComposeList

  7.7-177 AddProjectionInFactorOfDirectProduct

  7.7-178 AddProjectionInFactorOfDirectProductWithGivenDirectProduct

  7.7-179 AddProjectionInFactorOfDirectSum

  7.7-180 AddProjectionInFactorOfDirectSumWithGivenDirectSum

  7.7-181 AddProjectionInFactorOfFiberProduct

  7.7-182 AddProjectionInFactorOfFiberProductWithGivenFiberProduct

  7.7-183 AddProjectionOntoCoequalizer

  7.7-184 AddProjectionOntoCoequalizerWithGivenCoequalizer

  7.7-185 AddProjectiveDimension

  7.7-186 AddProjectiveLift

  7.7-187 AddPushout

  7.7-188 AddPushoutFunctorial

  7.7-189 AddPushoutFunctorialWithGivenPushouts

  7.7-190 AddRandomMorphismByInteger

  7.7-191 AddRandomMorphismByList

  7.7-192 AddRandomMorphismWithFixedRangeByInteger

  7.7-193 AddRandomMorphismWithFixedRangeByList

  7.7-194 AddRandomMorphismWithFixedSourceAndRangeByInteger

  7.7-195 AddRandomMorphismWithFixedSourceAndRangeByList

  7.7-196 AddRandomMorphismWithFixedSourceByInteger

  7.7-197 AddRandomMorphismWithFixedSourceByList

  7.7-198 AddRandomObjectByInteger

  7.7-199 AddRandomObjectByList

  7.7-200 AddSimplifyEndo

  7.7-201 AddSimplifyEndo_IsoFromInputObject

  7.7-202 AddSimplifyEndo_IsoToInputObject

  7.7-203 AddSimplifyMorphism

  7.7-204 AddSimplifyObject

  7.7-205 AddSimplifyObject_IsoFromInputObject

  7.7-206 AddSimplifyObject_IsoToInputObject

  7.7-207 AddSimplifyRange

  7.7-208 AddSimplifyRange_IsoFromInputObject

  7.7-209 AddSimplifyRange_IsoToInputObject

  7.7-210 AddSimplifySource

  7.7-211 AddSimplifySourceAndRange

  7.7-212 AddSimplifySourceAndRange_IsoFromInputRange

  7.7-213 AddSimplifySourceAndRange_IsoFromInputSource

  7.7-214 AddSimplifySourceAndRange_IsoToInputRange

  7.7-215 AddSimplifySourceAndRange_IsoToInputSource

  7.7-216 AddSimplifySource_IsoFromInputObject

  7.7-217 AddSimplifySource_IsoToInputObject

  7.7-218 AddSolveLinearSystemInAbCategory

  7.7-219 AddSolveLinearSystemInAbCategoryOrFail

  7.7-220 AddSomeInjectiveObject

  7.7-221 AddSomeProjectiveObject

  7.7-222 AddSomeReductionBySplitEpiSummand

  7.7-223 AddSomeReductionBySplitEpiSummand_MorphismFromInputRange

  7.7-224 AddSomeReductionBySplitEpiSummand_MorphismToInputRange

  7.7-225 AddSubtractionForMorphisms

  7.7-226 AddTerminalObject

  7.7-227 AddTerminalObjectFunctorial

  7.7-228 AddTerminalObjectFunctorialWithGivenTerminalObjects

  7.7-229 AddUniversalMorphismFromCoequalizer

  7.7-230 AddUniversalMorphismFromCoequalizerWithGivenCoequalizer

  7.7-231 AddUniversalMorphismFromCoproduct

  7.7-232 AddUniversalMorphismFromCoproductWithGivenCoproduct

  7.7-233 AddUniversalMorphismFromDirectSum

  7.7-234 AddUniversalMorphismFromDirectSumWithGivenDirectSum

  7.7-235 AddUniversalMorphismFromImage

  7.7-236 AddUniversalMorphismFromImageWithGivenImageObject

  7.7-237 AddUniversalMorphismFromInitialObject

  7.7-238 AddUniversalMorphismFromInitialObjectWithGivenInitialObject

  7.7-239 AddUniversalMorphismFromPushout

  7.7-240 AddUniversalMorphismFromPushoutWithGivenPushout

  7.7-241 AddUniversalMorphismFromZeroObject

  7.7-242 AddUniversalMorphismFromZeroObjectWithGivenZeroObject

  7.7-243 AddUniversalMorphismIntoCoimage

  7.7-244 AddUniversalMorphismIntoCoimageWithGivenCoimageObject

  7.7-245 AddUniversalMorphismIntoDirectProduct

  7.7-246 AddUniversalMorphismIntoDirectProductWithGivenDirectProduct

  7.7-247 AddUniversalMorphismIntoDirectSum

  7.7-248 AddUniversalMorphismIntoDirectSumWithGivenDirectSum

  7.7-249 AddUniversalMorphismIntoEqualizer

  7.7-250 AddUniversalMorphismIntoEqualizerWithGivenEqualizer

  7.7-251 AddUniversalMorphismIntoFiberProduct

  7.7-252 AddUniversalMorphismIntoFiberProductWithGivenFiberProduct

  7.7-253 AddUniversalMorphismIntoTerminalObject

  7.7-254 AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject

  7.7-255 AddUniversalMorphismIntoZeroObject

  7.7-256 AddUniversalMorphismIntoZeroObjectWithGivenZeroObject

  7.7-257 AddVerticalPostCompose

  7.7-258 AddVerticalPreCompose

  7.7-259 AddZeroMorphism

  7.7-260 AddZeroObject

  7.7-261 AddZeroObjectFunctorial

  7.7-262 AddZeroObjectFunctorialWithGivenZeroObjects

7 Add Functions

This section describes the overall structure of Add-functions and the functions installed by them.

7.1 Functions Installed by Add

Add functions have the following syntax:

DeclareOperation( "AddSomeFunc",
                  [ IsCapCategory, IsList, IsInt ] );

The first argument is the category to which some function (e.g. KernelObject) is added, the second is a list containing pairs of functions and additional filters for the arguments, (e.g. if one argument is a morphism, an additional filter could be IsMomomorphism). The third is an optional weight which will then be the weight for SomeFunc (default value: 100). This is described later. If only one function is to be installed, the list can be replaced by the function. CAP installs the given function(s) as methods for SomeFunc (resp. SomeFuncOp if SomeFunc is not an operation).

All installed methods follow the following steps, described below:

Every other part, except from function, does only depend on the name SomeFunc. We now explain the steps in detail.

7.2 Add Method

Except from installing a new method for the name SomeFunc, an Add method does slightly more. Every Add method has the same structure. The steps in the Add method are as follows:

After calling an add method, the corresponding operation is available in the category. Also, some derivations, which are triggered by the setting of the primitive value, might be available.

7.3 InstallAdd Function

Almost all Add methods in the CAP kernel are installed by the CapInternalInstallAdd operation. The definition of this function is as follows:

DeclareOperation( "CapInternalInstallAdd",
                  [ IsRecord ] );

The record can have the following components, most of which can be set in the method name record, used as described:

    [
        "object",
        "object_or_fail",
        "morphism",
        "morphism_or_fail",
        "twocell",
        "object_in_range_category_of_homomorphism_structure",
        "morphism_in_range_category_of_homomorphism_structure",
        "bool",
        "other_object",
        "other_morphism",
        "list_of_morphisms",
        "list_of_morphisms_or_fail",
        "nonneg_integer_or_infinity",
        "list_of_objects"
    ]

Using all those entries, the operation CapInternalInstallAdd installs add methods as described above. It first provides plausibility checks for all the entries described, then installs the Add method in 4 ways, with list or functions as second argument, and with an optional third parameter for the weight.

7.3-1 CapInternalInstallAdd
‣ CapInternalInstallAdd( record )( function )

See 7.3.

7.4 Enhancing the method name record

The function CAP_INTERNAL_ENHANCE_NAME_RECORD can be applied to a method name record to make the following enhancements:

7.5 Install All Adds

The function CAP_INTERNAL_INSTALL_ALL_ADDS does not take any arguments. It is an auxiliary function which first applies CAP_INTERNAL_ENHANCE_NAME_RECORD to CAP_INTERNAL_METHOD_NAME_RECORD. Afterwards it iterates over CAP_INTERNAL_METHOD_NAME_RECORD and calls the CapInternalInstallAdd with the corresponding method record entry except if the no_install component of the record is set to true.

7.6 Prepare functions

7.6-1 CAPOperationPrepareFunction
‣ CAPOperationPrepareFunction( prepare_function, category, func )( function )

Returns: a function

Given a non-CAP-conform function for any of the categorical operations, i.e., a function that computes the direct sum of two objects instead of a list of objects, this function wraps the function with a wrapper function to fit in the CAP context. For the mentioned binary direct sum one can call this function with "BinaryDirectSumToDirectSum" as prepare_function, the category, and the binary direct sum function. The function then returns a function that can be used for the direct sum categorical operation.

Note that func is not handled by the CAP caching mechanism and that the use of prepare functions is incompatible with WithGiven operations. Thus, one has to ensure manually that the equality and typing specifications are fulfilled.

7.6-2 CAPAddPrepareFunction
‣ CAPAddPrepareFunction( prepare_function, name, doc_string[, precondition_list] )( function )

Adds a prepare function to the list of CAP's prepare functions. The first argument is the prepare function itself. It should always be a function that takes a category and a function and returns a function. The argument name is the name of the prepare function, which is used in CAPOperationPrepareFunction. The argument doc_string should be a short string describing the functions. The optional argument precondition_list can describe preconditions for the prepare function to work, i.e., if the category does need to have PreCompose computable. This information is also recovered automatically from the prepare function itself, so the precondition_list is only necessary if the function needed is not explicitly used in the prepare function, e.g., if you use + instead of AdditionForMorphisms.

7.6-3 ListCAPPrepareFunctions
‣ ListCAPPrepareFunctions( arg )( function )

Lists all prepare functions.

7.7 Available Add functions

7.7-1 AddAdditionForMorphisms
‣ AddAdditionForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation AdditionForMorphisms. \(F: ( a, b ) \mapsto \mathtt{AdditionForMorphisms}(a, b)\).

7.7-2 AddAdditiveGenerators
‣ AddAdditiveGenerators( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation AdditiveGenerators. \(F: ( ) \mapsto \mathtt{AdditiveGenerators}()\).

7.7-3 AddAdditiveInverseForMorphisms
‣ AddAdditiveInverseForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation AdditiveInverseForMorphisms. \(F: ( a ) \mapsto \mathtt{AdditiveInverseForMorphisms}(a)\).

7.7-4 AddAstrictionToCoimage
‣ AddAstrictionToCoimage( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation AstrictionToCoimage. \(F: ( alpha ) \mapsto \mathtt{AstrictionToCoimage}(alpha)\).

7.7-5 AddAstrictionToCoimageWithGivenCoimageObject
‣ AddAstrictionToCoimageWithGivenCoimageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation AstrictionToCoimageWithGivenCoimageObject. \(F: ( alpha, C ) \mapsto \mathtt{AstrictionToCoimageWithGivenCoimageObject}(alpha, C)\).

7.7-6 AddBasisOfExternalHom
‣ AddBasisOfExternalHom( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation BasisOfExternalHom. \(F: ( arg2, arg3 ) \mapsto \mathtt{BasisOfExternalHom}(arg2, arg3)\).

7.7-7 AddCanonicalIdentificationFromCoimageToImageObject
‣ AddCanonicalIdentificationFromCoimageToImageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CanonicalIdentificationFromCoimageToImageObject. \(F: ( alpha ) \mapsto \mathtt{CanonicalIdentificationFromCoimageToImageObject}(alpha)\).

7.7-8 AddCanonicalIdentificationFromImageObjectToCoimage
‣ AddCanonicalIdentificationFromImageObjectToCoimage( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CanonicalIdentificationFromImageObjectToCoimage. \(F: ( alpha ) \mapsto \mathtt{CanonicalIdentificationFromImageObjectToCoimage}(alpha)\).

7.7-9 AddCoastrictionToImage
‣ AddCoastrictionToImage( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoastrictionToImage. \(F: ( alpha ) \mapsto \mathtt{CoastrictionToImage}(alpha)\).

7.7-10 AddCoastrictionToImageWithGivenImageObject
‣ AddCoastrictionToImageWithGivenImageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoastrictionToImageWithGivenImageObject. \(F: ( alpha, I ) \mapsto \mathtt{CoastrictionToImageWithGivenImageObject}(alpha, I)\).

7.7-11 AddCoefficientsOfMorphismWithGivenBasisOfExternalHom
‣ AddCoefficientsOfMorphismWithGivenBasisOfExternalHom( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoefficientsOfMorphismWithGivenBasisOfExternalHom. \(F: ( arg2, arg3 ) \mapsto \mathtt{CoefficientsOfMorphismWithGivenBasisOfExternalHom}(arg2, arg3)\).

7.7-12 AddCoequalizer
‣ AddCoequalizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation Coequalizer. \(F: ( arg2 ) \mapsto \mathtt{Coequalizer}(arg2)\).

7.7-13 AddCoequalizerFunctorial
‣ AddCoequalizerFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoequalizerFunctorial. \(F: ( morphisms, mu, morphismsp ) \mapsto \mathtt{CoequalizerFunctorial}(morphisms, mu, morphismsp)\).

7.7-14 AddCoequalizerFunctorialWithGivenCoequalizers
‣ AddCoequalizerFunctorialWithGivenCoequalizers( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoequalizerFunctorialWithGivenCoequalizers. \(F: ( P, morphisms, mu, morphismsp, Pp ) \mapsto \mathtt{CoequalizerFunctorialWithGivenCoequalizers}(P, morphisms, mu, morphismsp, Pp)\).

7.7-15 AddCoimageObject
‣ AddCoimageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoimageObject. \(F: ( arg2 ) \mapsto \mathtt{CoimageObject}(arg2)\).

7.7-16 AddCoimageProjection
‣ AddCoimageProjection( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoimageProjection. \(F: ( alpha ) \mapsto \mathtt{CoimageProjection}(alpha)\).

7.7-17 AddCoimageProjectionWithGivenCoimageObject
‣ AddCoimageProjectionWithGivenCoimageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoimageProjectionWithGivenCoimageObject. \(F: ( alpha, C ) \mapsto \mathtt{CoimageProjectionWithGivenCoimageObject}(alpha, C)\).

7.7-18 AddCokernelColift
‣ AddCokernelColift( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CokernelColift. \(F: ( alpha, T, tau ) \mapsto \mathtt{CokernelColift}(alpha, T, tau)\).

7.7-19 AddCokernelColiftWithGivenCokernelObject
‣ AddCokernelColiftWithGivenCokernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CokernelColiftWithGivenCokernelObject. \(F: ( alpha, T, tau, P ) \mapsto \mathtt{CokernelColiftWithGivenCokernelObject}(alpha, T, tau, P)\).

7.7-20 AddCokernelObject
‣ AddCokernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CokernelObject. \(F: ( arg2 ) \mapsto \mathtt{CokernelObject}(arg2)\).

7.7-21 AddCokernelObjectFunctorial
‣ AddCokernelObjectFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CokernelObjectFunctorial. \(F: ( alpha, mu, alphap ) \mapsto \mathtt{CokernelObjectFunctorial}(alpha, mu, alphap)\).

7.7-22 AddCokernelObjectFunctorialWithGivenCokernelObjects
‣ AddCokernelObjectFunctorialWithGivenCokernelObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CokernelObjectFunctorialWithGivenCokernelObjects. \(F: ( P, alpha, mu, alphap, Pp ) \mapsto \mathtt{CokernelObjectFunctorialWithGivenCokernelObjects}(P, alpha, mu, alphap, Pp)\).

7.7-23 AddCokernelProjection
‣ AddCokernelProjection( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CokernelProjection. \(F: ( alpha ) \mapsto \mathtt{CokernelProjection}(alpha)\).

7.7-24 AddCokernelProjectionWithGivenCokernelObject
‣ AddCokernelProjectionWithGivenCokernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CokernelProjectionWithGivenCokernelObject. \(F: ( alpha, P ) \mapsto \mathtt{CokernelProjectionWithGivenCokernelObject}(alpha, P)\).

7.7-25 AddColift
‣ AddColift( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation Colift. \(F: ( alpha, beta ) \mapsto \mathtt{Colift}(alpha, beta)\).

7.7-26 AddColiftAlongEpimorphism
‣ AddColiftAlongEpimorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ColiftAlongEpimorphism. \(F: ( epsilon, tau ) \mapsto \mathtt{ColiftAlongEpimorphism}(epsilon, tau)\).

7.7-27 AddColiftOrFail
‣ AddColiftOrFail( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ColiftOrFail. \(F: ( alpha, beta ) \mapsto \mathtt{ColiftOrFail}(alpha, beta)\).

7.7-28 AddComponentOfMorphismFromDirectSum
‣ AddComponentOfMorphismFromDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ComponentOfMorphismFromDirectSum. \(F: ( alpha, S, i ) \mapsto \mathtt{ComponentOfMorphismFromDirectSum}(alpha, S, i)\).

7.7-29 AddComponentOfMorphismIntoDirectSum
‣ AddComponentOfMorphismIntoDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ComponentOfMorphismIntoDirectSum. \(F: ( alpha, S, i ) \mapsto \mathtt{ComponentOfMorphismIntoDirectSum}(alpha, S, i)\).

7.7-30 AddCoproduct
‣ AddCoproduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation Coproduct. \(F: ( arg2 ) \mapsto \mathtt{Coproduct}(arg2)\).

7.7-31 AddCoproductFunctorial
‣ AddCoproductFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoproductFunctorial. \(F: ( objects, L, objectsp ) \mapsto \mathtt{CoproductFunctorial}(objects, L, objectsp)\).

7.7-32 AddCoproductFunctorialWithGivenCoproducts
‣ AddCoproductFunctorialWithGivenCoproducts( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation CoproductFunctorialWithGivenCoproducts. \(F: ( P, objects, L, objectsp, Pp ) \mapsto \mathtt{CoproductFunctorialWithGivenCoproducts}(P, objects, L, objectsp, Pp)\).

7.7-33 AddDirectProduct
‣ AddDirectProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectProduct. \(F: ( arg2 ) \mapsto \mathtt{DirectProduct}(arg2)\).

7.7-34 AddDirectProductFunctorial
‣ AddDirectProductFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectProductFunctorial. \(F: ( objects, L, objectsp ) \mapsto \mathtt{DirectProductFunctorial}(objects, L, objectsp)\).

7.7-35 AddDirectProductFunctorialWithGivenDirectProducts
‣ AddDirectProductFunctorialWithGivenDirectProducts( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectProductFunctorialWithGivenDirectProducts. \(F: ( P, objects, L, objectsp, Pp ) \mapsto \mathtt{DirectProductFunctorialWithGivenDirectProducts}(P, objects, L, objectsp, Pp)\).

7.7-36 AddDirectSum
‣ AddDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectSum. \(F: ( arg2 ) \mapsto \mathtt{DirectSum}(arg2)\).

7.7-37 AddDirectSumCodiagonalDifference
‣ AddDirectSumCodiagonalDifference( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectSumCodiagonalDifference. \(F: ( D ) \mapsto \mathtt{DirectSumCodiagonalDifference}(D)\).

7.7-38 AddDirectSumDiagonalDifference
‣ AddDirectSumDiagonalDifference( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectSumDiagonalDifference. \(F: ( D ) \mapsto \mathtt{DirectSumDiagonalDifference}(D)\).

7.7-39 AddDirectSumFunctorial
‣ AddDirectSumFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectSumFunctorial. \(F: ( objects, L, objectsp ) \mapsto \mathtt{DirectSumFunctorial}(objects, L, objectsp)\).

7.7-40 AddDirectSumFunctorialWithGivenDirectSums
‣ AddDirectSumFunctorialWithGivenDirectSums( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectSumFunctorialWithGivenDirectSums. \(F: ( P, objects, L, objectsp, Pp ) \mapsto \mathtt{DirectSumFunctorialWithGivenDirectSums}(P, objects, L, objectsp, Pp)\).

7.7-41 AddDirectSumProjectionInPushout
‣ AddDirectSumProjectionInPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DirectSumProjectionInPushout. \(F: ( D ) \mapsto \mathtt{DirectSumProjectionInPushout}(D)\).

7.7-42 AddDistinguishedObjectOfHomomorphismStructure
‣ AddDistinguishedObjectOfHomomorphismStructure( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation DistinguishedObjectOfHomomorphismStructure. \(F: ( ) \mapsto \mathtt{DistinguishedObjectOfHomomorphismStructure}()\).

7.7-43 AddEmbeddingOfEqualizer
‣ AddEmbeddingOfEqualizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation EmbeddingOfEqualizer. \(F: ( morphisms ) \mapsto \mathtt{EmbeddingOfEqualizer}(morphisms)\).

7.7-44 AddEmbeddingOfEqualizerWithGivenEqualizer
‣ AddEmbeddingOfEqualizerWithGivenEqualizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation EmbeddingOfEqualizerWithGivenEqualizer. \(F: ( morphisms, P ) \mapsto \mathtt{EmbeddingOfEqualizerWithGivenEqualizer}(morphisms, P)\).

7.7-45 AddEpimorphismFromSomeProjectiveObject
‣ AddEpimorphismFromSomeProjectiveObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation EpimorphismFromSomeProjectiveObject. \(F: ( A ) \mapsto \mathtt{EpimorphismFromSomeProjectiveObject}(A)\).

7.7-46 AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject
‣ AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject. \(F: ( A, P ) \mapsto \mathtt{EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject}(A, P)\).

7.7-47 AddEqualizer
‣ AddEqualizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation Equalizer. \(F: ( arg2 ) \mapsto \mathtt{Equalizer}(arg2)\).

7.7-48 AddEqualizerFunctorial
‣ AddEqualizerFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation EqualizerFunctorial. \(F: ( morphisms, mu, morphismsp ) \mapsto \mathtt{EqualizerFunctorial}(morphisms, mu, morphismsp)\).

7.7-49 AddEqualizerFunctorialWithGivenEqualizers
‣ AddEqualizerFunctorialWithGivenEqualizers( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation EqualizerFunctorialWithGivenEqualizers. \(F: ( P, morphisms, mu, morphismsp, Pp ) \mapsto \mathtt{EqualizerFunctorialWithGivenEqualizers}(P, morphisms, mu, morphismsp, Pp)\).

7.7-50 AddFiberProduct
‣ AddFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation FiberProduct. \(F: ( arg2 ) \mapsto \mathtt{FiberProduct}(arg2)\).

7.7-51 AddFiberProductEmbeddingInDirectSum
‣ AddFiberProductEmbeddingInDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation FiberProductEmbeddingInDirectSum. \(F: ( D ) \mapsto \mathtt{FiberProductEmbeddingInDirectSum}(D)\).

7.7-52 AddFiberProductFunctorial
‣ AddFiberProductFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation FiberProductFunctorial. \(F: ( morphisms, L, morphismsp ) \mapsto \mathtt{FiberProductFunctorial}(morphisms, L, morphismsp)\).

7.7-53 AddFiberProductFunctorialWithGivenFiberProducts
‣ AddFiberProductFunctorialWithGivenFiberProducts( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation FiberProductFunctorialWithGivenFiberProducts. \(F: ( P, morphisms, L, morphismsp, Pp ) \mapsto \mathtt{FiberProductFunctorialWithGivenFiberProducts}(P, morphisms, L, morphismsp, Pp)\).

7.7-54 AddHomologyObject
‣ AddHomologyObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation HomologyObject. \(F: ( alpha, beta ) \mapsto \mathtt{HomologyObject}(alpha, beta)\).

7.7-55 AddHomologyObjectFunctorialWithGivenHomologyObjects
‣ AddHomologyObjectFunctorialWithGivenHomologyObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation HomologyObjectFunctorialWithGivenHomologyObjects. \(F: ( H_1, L, H_2 ) \mapsto \mathtt{HomologyObjectFunctorialWithGivenHomologyObjects}(H_1, L, H_2)\).

7.7-56 AddHomomorphismStructureOnMorphisms
‣ AddHomomorphismStructureOnMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation HomomorphismStructureOnMorphisms. \(F: ( alpha, beta ) \mapsto \mathtt{HomomorphismStructureOnMorphisms}(alpha, beta)\).

7.7-57 AddHomomorphismStructureOnMorphismsWithGivenObjects
‣ AddHomomorphismStructureOnMorphismsWithGivenObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation HomomorphismStructureOnMorphismsWithGivenObjects. \(F: ( source, alpha, beta, range ) \mapsto \mathtt{HomomorphismStructureOnMorphismsWithGivenObjects}(source, alpha, beta, range)\).

7.7-58 AddHomomorphismStructureOnObjects
‣ AddHomomorphismStructureOnObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation HomomorphismStructureOnObjects. \(F: ( arg2, arg3 ) \mapsto \mathtt{HomomorphismStructureOnObjects}(arg2, arg3)\).

7.7-59 AddHorizontalPostCompose
‣ AddHorizontalPostCompose( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation HorizontalPostCompose. \(F: ( arg2, arg3 ) \mapsto \mathtt{HorizontalPostCompose}(arg2, arg3)\).

7.7-60 AddHorizontalPreCompose
‣ AddHorizontalPreCompose( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation HorizontalPreCompose. \(F: ( arg2, arg3 ) \mapsto \mathtt{HorizontalPreCompose}(arg2, arg3)\).

7.7-61 AddIdentityMorphism
‣ AddIdentityMorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IdentityMorphism. \(F: ( a ) \mapsto \mathtt{IdentityMorphism}(a)\).

7.7-62 AddIdentityTwoCell
‣ AddIdentityTwoCell( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IdentityTwoCell. \(F: ( arg2 ) \mapsto \mathtt{IdentityTwoCell}(arg2)\).

7.7-63 AddImageEmbedding
‣ AddImageEmbedding( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ImageEmbedding. \(F: ( alpha ) \mapsto \mathtt{ImageEmbedding}(alpha)\).

7.7-64 AddImageEmbeddingWithGivenImageObject
‣ AddImageEmbeddingWithGivenImageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ImageEmbeddingWithGivenImageObject. \(F: ( alpha, I ) \mapsto \mathtt{ImageEmbeddingWithGivenImageObject}(alpha, I)\).

7.7-65 AddImageObject
‣ AddImageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ImageObject. \(F: ( arg2 ) \mapsto \mathtt{ImageObject}(arg2)\).

7.7-66 AddInitialObject
‣ AddInitialObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InitialObject. \(F: ( ) \mapsto \mathtt{InitialObject}()\).

7.7-67 AddInitialObjectFunctorial
‣ AddInitialObjectFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InitialObjectFunctorial. \(F: ( ) \mapsto \mathtt{InitialObjectFunctorial}()\).

7.7-68 AddInitialObjectFunctorialWithGivenInitialObjects
‣ AddInitialObjectFunctorialWithGivenInitialObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InitialObjectFunctorialWithGivenInitialObjects. \(F: ( P, Pp ) \mapsto \mathtt{InitialObjectFunctorialWithGivenInitialObjects}(P, Pp)\).

7.7-69 AddInjectionOfCofactorOfCoproduct
‣ AddInjectionOfCofactorOfCoproduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectionOfCofactorOfCoproduct. \(F: ( objects, k ) \mapsto \mathtt{InjectionOfCofactorOfCoproduct}(objects, k)\).

7.7-70 AddInjectionOfCofactorOfCoproductWithGivenCoproduct
‣ AddInjectionOfCofactorOfCoproductWithGivenCoproduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectionOfCofactorOfCoproductWithGivenCoproduct. \(F: ( objects, k, P ) \mapsto \mathtt{InjectionOfCofactorOfCoproductWithGivenCoproduct}(objects, k, P)\).

7.7-71 AddInjectionOfCofactorOfDirectSum
‣ AddInjectionOfCofactorOfDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectionOfCofactorOfDirectSum. \(F: ( objects, k ) \mapsto \mathtt{InjectionOfCofactorOfDirectSum}(objects, k)\).

7.7-72 AddInjectionOfCofactorOfDirectSumWithGivenDirectSum
‣ AddInjectionOfCofactorOfDirectSumWithGivenDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectionOfCofactorOfDirectSumWithGivenDirectSum. \(F: ( objects, k, P ) \mapsto \mathtt{InjectionOfCofactorOfDirectSumWithGivenDirectSum}(objects, k, P)\).

7.7-73 AddInjectionOfCofactorOfPushout
‣ AddInjectionOfCofactorOfPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectionOfCofactorOfPushout. \(F: ( morphisms, k ) \mapsto \mathtt{InjectionOfCofactorOfPushout}(morphisms, k)\).

7.7-74 AddInjectionOfCofactorOfPushoutWithGivenPushout
‣ AddInjectionOfCofactorOfPushoutWithGivenPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectionOfCofactorOfPushoutWithGivenPushout. \(F: ( morphisms, k, P ) \mapsto \mathtt{InjectionOfCofactorOfPushoutWithGivenPushout}(morphisms, k, P)\).

7.7-75 AddInjectiveColift
‣ AddInjectiveColift( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectiveColift. \(F: ( alpha, beta ) \mapsto \mathtt{InjectiveColift}(alpha, beta)\).

7.7-76 AddInjectiveDimension
‣ AddInjectiveDimension( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InjectiveDimension. \(F: ( arg2 ) \mapsto \mathtt{InjectiveDimension}(arg2)\).

7.7-77 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure
‣ AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure. \(F: ( alpha ) \mapsto \mathtt{InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure}(alpha)\).

7.7-78 AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects
‣ AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects. \(F: ( source, alpha, range ) \mapsto \mathtt{InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects}(source, alpha, range)\).

7.7-79 AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism
‣ AddInterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism. \(F: ( arg2, arg3, arg4 ) \mapsto \mathtt{InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism}(arg2, arg3, arg4)\).

7.7-80 AddInverseForMorphisms
‣ AddInverseForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseForMorphisms. \(F: ( alpha ) \mapsto \mathtt{InverseForMorphisms}(alpha)\).

7.7-81 AddInverseMorphismFromCoimageToImageWithGivenObjects
‣ AddInverseMorphismFromCoimageToImageWithGivenObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation InverseMorphismFromCoimageToImageWithGivenObjects. \(F: ( C, alpha, I ) \mapsto \mathtt{InverseMorphismFromCoimageToImageWithGivenObjects}(C, alpha, I)\).

7.7-82 AddIsAutomorphism
‣ AddIsAutomorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsAutomorphism. \(F: ( arg2 ) \mapsto \mathtt{IsAutomorphism}(arg2)\).

7.7-83 AddIsBijectiveObject
‣ AddIsBijectiveObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsBijectiveObject. \(F: ( arg2 ) \mapsto \mathtt{IsBijectiveObject}(arg2)\).

7.7-84 AddIsCodominating
‣ AddIsCodominating( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsCodominating. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsCodominating}(arg2, arg3)\).

7.7-85 AddIsColiftable
‣ AddIsColiftable( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsColiftable. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsColiftable}(arg2, arg3)\).

7.7-86 AddIsColiftableAlongEpimorphism
‣ AddIsColiftableAlongEpimorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsColiftableAlongEpimorphism. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsColiftableAlongEpimorphism}(arg2, arg3)\).

7.7-87 AddIsCongruentForMorphisms
‣ AddIsCongruentForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsCongruentForMorphisms. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsCongruentForMorphisms}(arg2, arg3)\).

7.7-88 AddIsDominating
‣ AddIsDominating( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsDominating. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsDominating}(arg2, arg3)\).

7.7-89 AddIsEndomorphism
‣ AddIsEndomorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEndomorphism. \(F: ( arg2 ) \mapsto \mathtt{IsEndomorphism}(arg2)\).

7.7-90 AddIsEpimorphism
‣ AddIsEpimorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEpimorphism. \(F: ( arg2 ) \mapsto \mathtt{IsEpimorphism}(arg2)\).

7.7-91 AddIsEqualAsFactorobjects
‣ AddIsEqualAsFactorobjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualAsFactorobjects. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualAsFactorobjects}(arg2, arg3)\).

7.7-92 AddIsEqualAsSubobjects
‣ AddIsEqualAsSubobjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualAsSubobjects. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualAsSubobjects}(arg2, arg3)\).

7.7-93 AddIsEqualForCacheForMorphisms
‣ AddIsEqualForCacheForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualForCacheForMorphisms. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualForCacheForMorphisms}(arg2, arg3)\).

7.7-94 AddIsEqualForCacheForObjects
‣ AddIsEqualForCacheForObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualForCacheForObjects. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualForCacheForObjects}(arg2, arg3)\).

7.7-95 AddIsEqualForMorphisms
‣ AddIsEqualForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualForMorphisms. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualForMorphisms}(arg2, arg3)\).

7.7-96 AddIsEqualForMorphismsOnMor
‣ AddIsEqualForMorphismsOnMor( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualForMorphismsOnMor. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualForMorphismsOnMor}(arg2, arg3)\).

7.7-97 AddIsEqualForObjects
‣ AddIsEqualForObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualForObjects. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualForObjects}(arg2, arg3)\).

7.7-98 AddIsEqualToIdentityMorphism
‣ AddIsEqualToIdentityMorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualToIdentityMorphism. \(F: ( arg2 ) \mapsto \mathtt{IsEqualToIdentityMorphism}(arg2)\).

7.7-99 AddIsEqualToZeroMorphism
‣ AddIsEqualToZeroMorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsEqualToZeroMorphism. \(F: ( arg2 ) \mapsto \mathtt{IsEqualToZeroMorphism}(arg2)\).

7.7-100 AddIsHomSetInhabited
‣ AddIsHomSetInhabited( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsHomSetInhabited. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsHomSetInhabited}(arg2, arg3)\).

7.7-101 AddIsIdempotent
‣ AddIsIdempotent( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsIdempotent. \(F: ( arg2 ) \mapsto \mathtt{IsIdempotent}(arg2)\).

7.7-102 AddIsInitial
‣ AddIsInitial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsInitial. \(F: ( arg2 ) \mapsto \mathtt{IsInitial}(arg2)\).

7.7-103 AddIsInjective
‣ AddIsInjective( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsInjective. \(F: ( arg2 ) \mapsto \mathtt{IsInjective}(arg2)\).

7.7-104 AddIsIsomorphism
‣ AddIsIsomorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsIsomorphism. \(F: ( arg2 ) \mapsto \mathtt{IsIsomorphism}(arg2)\).

7.7-105 AddIsLiftable
‣ AddIsLiftable( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsLiftable. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsLiftable}(arg2, arg3)\).

7.7-106 AddIsLiftableAlongMonomorphism
‣ AddIsLiftableAlongMonomorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsLiftableAlongMonomorphism. \(F: ( arg2, arg3 ) \mapsto \mathtt{IsLiftableAlongMonomorphism}(arg2, arg3)\).

7.7-107 AddIsMonomorphism
‣ AddIsMonomorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsMonomorphism. \(F: ( arg2 ) \mapsto \mathtt{IsMonomorphism}(arg2)\).

7.7-108 AddIsOne
‣ AddIsOne( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsOne. \(F: ( arg2 ) \mapsto \mathtt{IsOne}(arg2)\).

7.7-109 AddIsProjective
‣ AddIsProjective( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsProjective. \(F: ( arg2 ) \mapsto \mathtt{IsProjective}(arg2)\).

7.7-110 AddIsSplitEpimorphism
‣ AddIsSplitEpimorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsSplitEpimorphism. \(F: ( arg2 ) \mapsto \mathtt{IsSplitEpimorphism}(arg2)\).

7.7-111 AddIsSplitMonomorphism
‣ AddIsSplitMonomorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsSplitMonomorphism. \(F: ( arg2 ) \mapsto \mathtt{IsSplitMonomorphism}(arg2)\).

7.7-112 AddIsTerminal
‣ AddIsTerminal( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsTerminal. \(F: ( arg2 ) \mapsto \mathtt{IsTerminal}(arg2)\).

7.7-113 AddIsWellDefinedForMorphisms
‣ AddIsWellDefinedForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsWellDefinedForMorphisms. \(F: ( arg2 ) \mapsto \mathtt{IsWellDefinedForMorphisms}(arg2)\).

7.7-114 AddIsWellDefinedForObjects
‣ AddIsWellDefinedForObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsWellDefinedForObjects. \(F: ( arg2 ) \mapsto \mathtt{IsWellDefinedForObjects}(arg2)\).

7.7-115 AddIsWellDefinedForTwoCells
‣ AddIsWellDefinedForTwoCells( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsWellDefinedForTwoCells. \(F: ( arg2 ) \mapsto \mathtt{IsWellDefinedForTwoCells}(arg2)\).

7.7-116 AddIsZeroForMorphisms
‣ AddIsZeroForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsZeroForMorphisms. \(F: ( arg2 ) \mapsto \mathtt{IsZeroForMorphisms}(arg2)\).

7.7-117 AddIsZeroForObjects
‣ AddIsZeroForObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsZeroForObjects. \(F: ( arg2 ) \mapsto \mathtt{IsZeroForObjects}(arg2)\).

7.7-118 AddIsomorphismFromCoequalizerOfCoproductDiagramToPushout
‣ AddIsomorphismFromCoequalizerOfCoproductDiagramToPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromCoequalizerOfCoproductDiagramToPushout. \(F: ( D ) \mapsto \mathtt{IsomorphismFromCoequalizerOfCoproductDiagramToPushout}(D)\).

7.7-119 AddIsomorphismFromCoimageToCokernelOfKernel
‣ AddIsomorphismFromCoimageToCokernelOfKernel( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromCoimageToCokernelOfKernel. \(F: ( alpha ) \mapsto \mathtt{IsomorphismFromCoimageToCokernelOfKernel}(alpha)\).

7.7-120 AddIsomorphismFromCokernelOfDiagonalDifferenceToPushout
‣ AddIsomorphismFromCokernelOfDiagonalDifferenceToPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromCokernelOfDiagonalDifferenceToPushout. \(F: ( D ) \mapsto \mathtt{IsomorphismFromCokernelOfDiagonalDifferenceToPushout}(D)\).

7.7-121 AddIsomorphismFromCokernelOfKernelToCoimage
‣ AddIsomorphismFromCokernelOfKernelToCoimage( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromCokernelOfKernelToCoimage. \(F: ( alpha ) \mapsto \mathtt{IsomorphismFromCokernelOfKernelToCoimage}(alpha)\).

7.7-122 AddIsomorphismFromCoproductToDirectSum
‣ AddIsomorphismFromCoproductToDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromCoproductToDirectSum. \(F: ( D ) \mapsto \mathtt{IsomorphismFromCoproductToDirectSum}(D)\).

7.7-123 AddIsomorphismFromDirectProductToDirectSum
‣ AddIsomorphismFromDirectProductToDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromDirectProductToDirectSum. \(F: ( D ) \mapsto \mathtt{IsomorphismFromDirectProductToDirectSum}(D)\).

7.7-124 AddIsomorphismFromDirectSumToCoproduct
‣ AddIsomorphismFromDirectSumToCoproduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromDirectSumToCoproduct. \(F: ( D ) \mapsto \mathtt{IsomorphismFromDirectSumToCoproduct}(D)\).

7.7-125 AddIsomorphismFromDirectSumToDirectProduct
‣ AddIsomorphismFromDirectSumToDirectProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromDirectSumToDirectProduct. \(F: ( D ) \mapsto \mathtt{IsomorphismFromDirectSumToDirectProduct}(D)\).

7.7-126 AddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct
‣ AddIsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct. \(F: ( D ) \mapsto \mathtt{IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct}(D)\).

7.7-127 AddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram
‣ AddIsomorphismFromFiberProductToEqualizerOfDirectProductDiagram( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromFiberProductToEqualizerOfDirectProductDiagram. \(F: ( D ) \mapsto \mathtt{IsomorphismFromFiberProductToEqualizerOfDirectProductDiagram}(D)\).

7.7-128 AddIsomorphismFromFiberProductToKernelOfDiagonalDifference
‣ AddIsomorphismFromFiberProductToKernelOfDiagonalDifference( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromFiberProductToKernelOfDiagonalDifference. \(F: ( D ) \mapsto \mathtt{IsomorphismFromFiberProductToKernelOfDiagonalDifference}(D)\).

7.7-129 AddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject
‣ AddIsomorphismFromHomologyObjectToItsConstructionAsAnImageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromHomologyObjectToItsConstructionAsAnImageObject. \(F: ( alpha, beta ) \mapsto \mathtt{IsomorphismFromHomologyObjectToItsConstructionAsAnImageObject}(alpha, beta)\).

7.7-130 AddIsomorphismFromImageObjectToKernelOfCokernel
‣ AddIsomorphismFromImageObjectToKernelOfCokernel( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromImageObjectToKernelOfCokernel. \(F: ( alpha ) \mapsto \mathtt{IsomorphismFromImageObjectToKernelOfCokernel}(alpha)\).

7.7-131 AddIsomorphismFromInitialObjectToZeroObject
‣ AddIsomorphismFromInitialObjectToZeroObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromInitialObjectToZeroObject. \(F: ( ) \mapsto \mathtt{IsomorphismFromInitialObjectToZeroObject}()\).

7.7-132 AddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject
‣ AddIsomorphismFromItsConstructionAsAnImageObjectToHomologyObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromItsConstructionAsAnImageObjectToHomologyObject. \(F: ( alpha, beta ) \mapsto \mathtt{IsomorphismFromItsConstructionAsAnImageObjectToHomologyObject}(alpha, beta)\).

7.7-133 AddIsomorphismFromKernelOfCokernelToImageObject
‣ AddIsomorphismFromKernelOfCokernelToImageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromKernelOfCokernelToImageObject. \(F: ( alpha ) \mapsto \mathtt{IsomorphismFromKernelOfCokernelToImageObject}(alpha)\).

7.7-134 AddIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct
‣ AddIsomorphismFromKernelOfDiagonalDifferenceToFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromKernelOfDiagonalDifferenceToFiberProduct. \(F: ( D ) \mapsto \mathtt{IsomorphismFromKernelOfDiagonalDifferenceToFiberProduct}(D)\).

7.7-135 AddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram
‣ AddIsomorphismFromPushoutToCoequalizerOfCoproductDiagram( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromPushoutToCoequalizerOfCoproductDiagram. \(F: ( D ) \mapsto \mathtt{IsomorphismFromPushoutToCoequalizerOfCoproductDiagram}(D)\).

7.7-136 AddIsomorphismFromPushoutToCokernelOfDiagonalDifference
‣ AddIsomorphismFromPushoutToCokernelOfDiagonalDifference( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromPushoutToCokernelOfDiagonalDifference. \(F: ( D ) \mapsto \mathtt{IsomorphismFromPushoutToCokernelOfDiagonalDifference}(D)\).

7.7-137 AddIsomorphismFromTerminalObjectToZeroObject
‣ AddIsomorphismFromTerminalObjectToZeroObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromTerminalObjectToZeroObject. \(F: ( ) \mapsto \mathtt{IsomorphismFromTerminalObjectToZeroObject}()\).

7.7-138 AddIsomorphismFromZeroObjectToInitialObject
‣ AddIsomorphismFromZeroObjectToInitialObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromZeroObjectToInitialObject. \(F: ( ) \mapsto \mathtt{IsomorphismFromZeroObjectToInitialObject}()\).

7.7-139 AddIsomorphismFromZeroObjectToTerminalObject
‣ AddIsomorphismFromZeroObjectToTerminalObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation IsomorphismFromZeroObjectToTerminalObject. \(F: ( ) \mapsto \mathtt{IsomorphismFromZeroObjectToTerminalObject}()\).

7.7-140 AddKernelEmbedding
‣ AddKernelEmbedding( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation KernelEmbedding. \(F: ( alpha ) \mapsto \mathtt{KernelEmbedding}(alpha)\).

7.7-141 AddKernelEmbeddingWithGivenKernelObject
‣ AddKernelEmbeddingWithGivenKernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation KernelEmbeddingWithGivenKernelObject. \(F: ( alpha, P ) \mapsto \mathtt{KernelEmbeddingWithGivenKernelObject}(alpha, P)\).

7.7-142 AddKernelLift
‣ AddKernelLift( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation KernelLift. \(F: ( alpha, T, tau ) \mapsto \mathtt{KernelLift}(alpha, T, tau)\).

7.7-143 AddKernelLiftWithGivenKernelObject
‣ AddKernelLiftWithGivenKernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation KernelLiftWithGivenKernelObject. \(F: ( alpha, T, tau, P ) \mapsto \mathtt{KernelLiftWithGivenKernelObject}(alpha, T, tau, P)\).

7.7-144 AddKernelObject
‣ AddKernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation KernelObject. \(F: ( arg2 ) \mapsto \mathtt{KernelObject}(arg2)\).

7.7-145 AddKernelObjectFunctorial
‣ AddKernelObjectFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation KernelObjectFunctorial. \(F: ( alpha, mu, alphap ) \mapsto \mathtt{KernelObjectFunctorial}(alpha, mu, alphap)\).

7.7-146 AddKernelObjectFunctorialWithGivenKernelObjects
‣ AddKernelObjectFunctorialWithGivenKernelObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation KernelObjectFunctorialWithGivenKernelObjects. \(F: ( P, alpha, mu, alphap, Pp ) \mapsto \mathtt{KernelObjectFunctorialWithGivenKernelObjects}(P, alpha, mu, alphap, Pp)\).

7.7-147 AddLift
‣ AddLift( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation Lift. \(F: ( alpha, beta ) \mapsto \mathtt{Lift}(alpha, beta)\).

7.7-148 AddLiftAlongMonomorphism
‣ AddLiftAlongMonomorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation LiftAlongMonomorphism. \(F: ( iota, tau ) \mapsto \mathtt{LiftAlongMonomorphism}(iota, tau)\).

7.7-149 AddLiftOrFail
‣ AddLiftOrFail( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation LiftOrFail. \(F: ( alpha, beta ) \mapsto \mathtt{LiftOrFail}(alpha, beta)\).

7.7-150 AddMereExistenceOfSolutionOfLinearSystemInAbCategory
‣ AddMereExistenceOfSolutionOfLinearSystemInAbCategory( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MereExistenceOfSolutionOfLinearSystemInAbCategory. \(F: ( arg2, arg3, arg4 ) \mapsto \mathtt{MereExistenceOfSolutionOfLinearSystemInAbCategory}(arg2, arg3, arg4)\).

7.7-151 AddMonomorphismIntoSomeInjectiveObject
‣ AddMonomorphismIntoSomeInjectiveObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MonomorphismIntoSomeInjectiveObject. \(F: ( A ) \mapsto \mathtt{MonomorphismIntoSomeInjectiveObject}(A)\).

7.7-152 AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject
‣ AddMonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject. \(F: ( A, I ) \mapsto \mathtt{MonomorphismIntoSomeInjectiveObjectWithGivenSomeInjectiveObject}(A, I)\).

7.7-153 AddMorphismBetweenDirectSums
‣ AddMorphismBetweenDirectSums( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismBetweenDirectSums. \(F: ( source_diagram, mat, range_diagram ) \mapsto \mathtt{MorphismBetweenDirectSums}(source_diagram, mat, range_diagram)\).

7.7-154 AddMorphismBetweenDirectSumsWithGivenDirectSums
‣ AddMorphismBetweenDirectSumsWithGivenDirectSums( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismBetweenDirectSumsWithGivenDirectSums. \(F: ( S, source_diagram, mat, range_diagram, T ) \mapsto \mathtt{MorphismBetweenDirectSumsWithGivenDirectSums}(S, source_diagram, mat, range_diagram, T)\).

7.7-155 AddMorphismConstructor
‣ AddMorphismConstructor( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismConstructor. \(F: ( arg2, arg3, arg4 ) \mapsto \mathtt{MorphismConstructor}(arg2, arg3, arg4)\).

7.7-156 AddMorphismDatum
‣ AddMorphismDatum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismDatum. \(F: ( arg2 ) \mapsto \mathtt{MorphismDatum}(arg2)\).

7.7-157 AddMorphismFromCoimageToImageWithGivenObjects
‣ AddMorphismFromCoimageToImageWithGivenObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromCoimageToImageWithGivenObjects. \(F: ( C, alpha, I ) \mapsto \mathtt{MorphismFromCoimageToImageWithGivenObjects}(C, alpha, I)\).

7.7-158 AddMorphismFromEqualizerToSink
‣ AddMorphismFromEqualizerToSink( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromEqualizerToSink. \(F: ( morphisms ) \mapsto \mathtt{MorphismFromEqualizerToSink}(morphisms)\).

7.7-159 AddMorphismFromEqualizerToSinkWithGivenEqualizer
‣ AddMorphismFromEqualizerToSinkWithGivenEqualizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromEqualizerToSinkWithGivenEqualizer. \(F: ( morphisms, P ) \mapsto \mathtt{MorphismFromEqualizerToSinkWithGivenEqualizer}(morphisms, P)\).

7.7-160 AddMorphismFromFiberProductToSink
‣ AddMorphismFromFiberProductToSink( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromFiberProductToSink. \(F: ( morphisms ) \mapsto \mathtt{MorphismFromFiberProductToSink}(morphisms)\).

7.7-161 AddMorphismFromFiberProductToSinkWithGivenFiberProduct
‣ AddMorphismFromFiberProductToSinkWithGivenFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromFiberProductToSinkWithGivenFiberProduct. \(F: ( morphisms, P ) \mapsto \mathtt{MorphismFromFiberProductToSinkWithGivenFiberProduct}(morphisms, P)\).

7.7-162 AddMorphismFromKernelObjectToSink
‣ AddMorphismFromKernelObjectToSink( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromKernelObjectToSink. \(F: ( alpha ) \mapsto \mathtt{MorphismFromKernelObjectToSink}(alpha)\).

7.7-163 AddMorphismFromKernelObjectToSinkWithGivenKernelObject
‣ AddMorphismFromKernelObjectToSinkWithGivenKernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromKernelObjectToSinkWithGivenKernelObject. \(F: ( alpha, P ) \mapsto \mathtt{MorphismFromKernelObjectToSinkWithGivenKernelObject}(alpha, P)\).

7.7-164 AddMorphismFromSourceToCoequalizer
‣ AddMorphismFromSourceToCoequalizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromSourceToCoequalizer. \(F: ( morphisms ) \mapsto \mathtt{MorphismFromSourceToCoequalizer}(morphisms)\).

7.7-165 AddMorphismFromSourceToCoequalizerWithGivenCoequalizer
‣ AddMorphismFromSourceToCoequalizerWithGivenCoequalizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromSourceToCoequalizerWithGivenCoequalizer. \(F: ( morphisms, P ) \mapsto \mathtt{MorphismFromSourceToCoequalizerWithGivenCoequalizer}(morphisms, P)\).

7.7-166 AddMorphismFromSourceToCokernelObject
‣ AddMorphismFromSourceToCokernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromSourceToCokernelObject. \(F: ( alpha ) \mapsto \mathtt{MorphismFromSourceToCokernelObject}(alpha)\).

7.7-167 AddMorphismFromSourceToCokernelObjectWithGivenCokernelObject
‣ AddMorphismFromSourceToCokernelObjectWithGivenCokernelObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromSourceToCokernelObjectWithGivenCokernelObject. \(F: ( alpha, P ) \mapsto \mathtt{MorphismFromSourceToCokernelObjectWithGivenCokernelObject}(alpha, P)\).

7.7-168 AddMorphismFromSourceToPushout
‣ AddMorphismFromSourceToPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromSourceToPushout. \(F: ( morphisms ) \mapsto \mathtt{MorphismFromSourceToPushout}(morphisms)\).

7.7-169 AddMorphismFromSourceToPushoutWithGivenPushout
‣ AddMorphismFromSourceToPushoutWithGivenPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MorphismFromSourceToPushoutWithGivenPushout. \(F: ( morphisms, P ) \mapsto \mathtt{MorphismFromSourceToPushoutWithGivenPushout}(morphisms, P)\).

7.7-170 AddMultiplyWithElementOfCommutativeRingForMorphisms
‣ AddMultiplyWithElementOfCommutativeRingForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation MultiplyWithElementOfCommutativeRingForMorphisms. \(F: ( r, a ) \mapsto \mathtt{MultiplyWithElementOfCommutativeRingForMorphisms}(r, a)\).

7.7-171 AddObjectConstructor
‣ AddObjectConstructor( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ObjectConstructor. \(F: ( arg2 ) \mapsto \mathtt{ObjectConstructor}(arg2)\).

7.7-172 AddObjectDatum
‣ AddObjectDatum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ObjectDatum. \(F: ( arg2 ) \mapsto \mathtt{ObjectDatum}(arg2)\).

7.7-173 AddPostCompose
‣ AddPostCompose( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation PostCompose. \(F: ( beta, alpha ) \mapsto \mathtt{PostCompose}(beta, alpha)\).

7.7-174 AddPostComposeList
‣ AddPostComposeList( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation PostComposeList. \(F: ( list_of_morphisms ) \mapsto \mathtt{PostComposeList}(list_of_morphisms)\).

7.7-175 AddPreCompose
‣ AddPreCompose( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation PreCompose. \(F: ( alpha, beta ) \mapsto \mathtt{PreCompose}(alpha, beta)\).

7.7-176 AddPreComposeList
‣ AddPreComposeList( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation PreComposeList. \(F: ( list_of_morphisms ) \mapsto \mathtt{PreComposeList}(list_of_morphisms)\).

7.7-177 AddProjectionInFactorOfDirectProduct
‣ AddProjectionInFactorOfDirectProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionInFactorOfDirectProduct. \(F: ( objects, k ) \mapsto \mathtt{ProjectionInFactorOfDirectProduct}(objects, k)\).

7.7-178 AddProjectionInFactorOfDirectProductWithGivenDirectProduct
‣ AddProjectionInFactorOfDirectProductWithGivenDirectProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionInFactorOfDirectProductWithGivenDirectProduct. \(F: ( objects, k, P ) \mapsto \mathtt{ProjectionInFactorOfDirectProductWithGivenDirectProduct}(objects, k, P)\).

7.7-179 AddProjectionInFactorOfDirectSum
‣ AddProjectionInFactorOfDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionInFactorOfDirectSum. \(F: ( objects, k ) \mapsto \mathtt{ProjectionInFactorOfDirectSum}(objects, k)\).

7.7-180 AddProjectionInFactorOfDirectSumWithGivenDirectSum
‣ AddProjectionInFactorOfDirectSumWithGivenDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionInFactorOfDirectSumWithGivenDirectSum. \(F: ( objects, k, P ) \mapsto \mathtt{ProjectionInFactorOfDirectSumWithGivenDirectSum}(objects, k, P)\).

7.7-181 AddProjectionInFactorOfFiberProduct
‣ AddProjectionInFactorOfFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionInFactorOfFiberProduct. \(F: ( morphisms, k ) \mapsto \mathtt{ProjectionInFactorOfFiberProduct}(morphisms, k)\).

7.7-182 AddProjectionInFactorOfFiberProductWithGivenFiberProduct
‣ AddProjectionInFactorOfFiberProductWithGivenFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionInFactorOfFiberProductWithGivenFiberProduct. \(F: ( morphisms, k, P ) \mapsto \mathtt{ProjectionInFactorOfFiberProductWithGivenFiberProduct}(morphisms, k, P)\).

7.7-183 AddProjectionOntoCoequalizer
‣ AddProjectionOntoCoequalizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionOntoCoequalizer. \(F: ( morphisms ) \mapsto \mathtt{ProjectionOntoCoequalizer}(morphisms)\).

7.7-184 AddProjectionOntoCoequalizerWithGivenCoequalizer
‣ AddProjectionOntoCoequalizerWithGivenCoequalizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectionOntoCoequalizerWithGivenCoequalizer. \(F: ( morphisms, P ) \mapsto \mathtt{ProjectionOntoCoequalizerWithGivenCoequalizer}(morphisms, P)\).

7.7-185 AddProjectiveDimension
‣ AddProjectiveDimension( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectiveDimension. \(F: ( arg2 ) \mapsto \mathtt{ProjectiveDimension}(arg2)\).

7.7-186 AddProjectiveLift
‣ AddProjectiveLift( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ProjectiveLift. \(F: ( alpha, beta ) \mapsto \mathtt{ProjectiveLift}(alpha, beta)\).

7.7-187 AddPushout
‣ AddPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation Pushout. \(F: ( arg2 ) \mapsto \mathtt{Pushout}(arg2)\).

7.7-188 AddPushoutFunctorial
‣ AddPushoutFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation PushoutFunctorial. \(F: ( morphisms, L, morphismsp ) \mapsto \mathtt{PushoutFunctorial}(morphisms, L, morphismsp)\).

7.7-189 AddPushoutFunctorialWithGivenPushouts
‣ AddPushoutFunctorialWithGivenPushouts( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation PushoutFunctorialWithGivenPushouts. \(F: ( P, morphisms, L, morphismsp, Pp ) \mapsto \mathtt{PushoutFunctorialWithGivenPushouts}(P, morphisms, L, morphismsp, Pp)\).

7.7-190 AddRandomMorphismByInteger
‣ AddRandomMorphismByInteger( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismByInteger. \(F: ( n ) \mapsto \mathtt{RandomMorphismByInteger}(n)\).

7.7-191 AddRandomMorphismByList
‣ AddRandomMorphismByList( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismByList. \(F: ( L ) \mapsto \mathtt{RandomMorphismByList}(L)\).

7.7-192 AddRandomMorphismWithFixedRangeByInteger
‣ AddRandomMorphismWithFixedRangeByInteger( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismWithFixedRangeByInteger. \(F: ( B, n ) \mapsto \mathtt{RandomMorphismWithFixedRangeByInteger}(B, n)\).

7.7-193 AddRandomMorphismWithFixedRangeByList
‣ AddRandomMorphismWithFixedRangeByList( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismWithFixedRangeByList. \(F: ( B, L ) \mapsto \mathtt{RandomMorphismWithFixedRangeByList}(B, L)\).

7.7-194 AddRandomMorphismWithFixedSourceAndRangeByInteger
‣ AddRandomMorphismWithFixedSourceAndRangeByInteger( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismWithFixedSourceAndRangeByInteger. \(F: ( A, B, n ) \mapsto \mathtt{RandomMorphismWithFixedSourceAndRangeByInteger}(A, B, n)\).

7.7-195 AddRandomMorphismWithFixedSourceAndRangeByList
‣ AddRandomMorphismWithFixedSourceAndRangeByList( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismWithFixedSourceAndRangeByList. \(F: ( A, B, L ) \mapsto \mathtt{RandomMorphismWithFixedSourceAndRangeByList}(A, B, L)\).

7.7-196 AddRandomMorphismWithFixedSourceByInteger
‣ AddRandomMorphismWithFixedSourceByInteger( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismWithFixedSourceByInteger. \(F: ( A, n ) \mapsto \mathtt{RandomMorphismWithFixedSourceByInteger}(A, n)\).

7.7-197 AddRandomMorphismWithFixedSourceByList
‣ AddRandomMorphismWithFixedSourceByList( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomMorphismWithFixedSourceByList. \(F: ( A, L ) \mapsto \mathtt{RandomMorphismWithFixedSourceByList}(A, L)\).

7.7-198 AddRandomObjectByInteger
‣ AddRandomObjectByInteger( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomObjectByInteger. \(F: ( n ) \mapsto \mathtt{RandomObjectByInteger}(n)\).

7.7-199 AddRandomObjectByList
‣ AddRandomObjectByList( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation RandomObjectByList. \(F: ( L ) \mapsto \mathtt{RandomObjectByList}(L)\).

7.7-200 AddSimplifyEndo
‣ AddSimplifyEndo( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyEndo. \(F: ( mor, n ) \mapsto \mathtt{SimplifyEndo}(mor, n)\).

7.7-201 AddSimplifyEndo_IsoFromInputObject
‣ AddSimplifyEndo_IsoFromInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyEndo_IsoFromInputObject. \(F: ( mor, n ) \mapsto \mathtt{SimplifyEndo_IsoFromInputObject}(mor, n)\).

7.7-202 AddSimplifyEndo_IsoToInputObject
‣ AddSimplifyEndo_IsoToInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyEndo_IsoToInputObject. \(F: ( mor, n ) \mapsto \mathtt{SimplifyEndo_IsoToInputObject}(mor, n)\).

7.7-203 AddSimplifyMorphism
‣ AddSimplifyMorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyMorphism. \(F: ( mor, n ) \mapsto \mathtt{SimplifyMorphism}(mor, n)\).

7.7-204 AddSimplifyObject
‣ AddSimplifyObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyObject. \(F: ( A, n ) \mapsto \mathtt{SimplifyObject}(A, n)\).

7.7-205 AddSimplifyObject_IsoFromInputObject
‣ AddSimplifyObject_IsoFromInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyObject_IsoFromInputObject. \(F: ( A, n ) \mapsto \mathtt{SimplifyObject_IsoFromInputObject}(A, n)\).

7.7-206 AddSimplifyObject_IsoToInputObject
‣ AddSimplifyObject_IsoToInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyObject_IsoToInputObject. \(F: ( A, n ) \mapsto \mathtt{SimplifyObject_IsoToInputObject}(A, n)\).

7.7-207 AddSimplifyRange
‣ AddSimplifyRange( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyRange. \(F: ( mor, n ) \mapsto \mathtt{SimplifyRange}(mor, n)\).

7.7-208 AddSimplifyRange_IsoFromInputObject
‣ AddSimplifyRange_IsoFromInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyRange_IsoFromInputObject. \(F: ( mor, n ) \mapsto \mathtt{SimplifyRange_IsoFromInputObject}(mor, n)\).

7.7-209 AddSimplifyRange_IsoToInputObject
‣ AddSimplifyRange_IsoToInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifyRange_IsoToInputObject. \(F: ( mor, n ) \mapsto \mathtt{SimplifyRange_IsoToInputObject}(mor, n)\).

7.7-210 AddSimplifySource
‣ AddSimplifySource( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySource. \(F: ( mor, n ) \mapsto \mathtt{SimplifySource}(mor, n)\).

7.7-211 AddSimplifySourceAndRange
‣ AddSimplifySourceAndRange( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySourceAndRange. \(F: ( mor, n ) \mapsto \mathtt{SimplifySourceAndRange}(mor, n)\).

7.7-212 AddSimplifySourceAndRange_IsoFromInputRange
‣ AddSimplifySourceAndRange_IsoFromInputRange( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySourceAndRange_IsoFromInputRange. \(F: ( mor, n ) \mapsto \mathtt{SimplifySourceAndRange_IsoFromInputRange}(mor, n)\).

7.7-213 AddSimplifySourceAndRange_IsoFromInputSource
‣ AddSimplifySourceAndRange_IsoFromInputSource( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySourceAndRange_IsoFromInputSource. \(F: ( mor, n ) \mapsto \mathtt{SimplifySourceAndRange_IsoFromInputSource}(mor, n)\).

7.7-214 AddSimplifySourceAndRange_IsoToInputRange
‣ AddSimplifySourceAndRange_IsoToInputRange( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySourceAndRange_IsoToInputRange. \(F: ( mor, n ) \mapsto \mathtt{SimplifySourceAndRange_IsoToInputRange}(mor, n)\).

7.7-215 AddSimplifySourceAndRange_IsoToInputSource
‣ AddSimplifySourceAndRange_IsoToInputSource( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySourceAndRange_IsoToInputSource. \(F: ( mor, n ) \mapsto \mathtt{SimplifySourceAndRange_IsoToInputSource}(mor, n)\).

7.7-216 AddSimplifySource_IsoFromInputObject
‣ AddSimplifySource_IsoFromInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySource_IsoFromInputObject. \(F: ( mor, n ) \mapsto \mathtt{SimplifySource_IsoFromInputObject}(mor, n)\).

7.7-217 AddSimplifySource_IsoToInputObject
‣ AddSimplifySource_IsoToInputObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SimplifySource_IsoToInputObject. \(F: ( mor, n ) \mapsto \mathtt{SimplifySource_IsoToInputObject}(mor, n)\).

7.7-218 AddSolveLinearSystemInAbCategory
‣ AddSolveLinearSystemInAbCategory( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SolveLinearSystemInAbCategory. \(F: ( arg2, arg3, arg4 ) \mapsto \mathtt{SolveLinearSystemInAbCategory}(arg2, arg3, arg4)\).

7.7-219 AddSolveLinearSystemInAbCategoryOrFail
‣ AddSolveLinearSystemInAbCategoryOrFail( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SolveLinearSystemInAbCategoryOrFail. \(F: ( arg2, arg3, arg4 ) \mapsto \mathtt{SolveLinearSystemInAbCategoryOrFail}(arg2, arg3, arg4)\).

7.7-220 AddSomeInjectiveObject
‣ AddSomeInjectiveObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SomeInjectiveObject. \(F: ( arg2 ) \mapsto \mathtt{SomeInjectiveObject}(arg2)\).

7.7-221 AddSomeProjectiveObject
‣ AddSomeProjectiveObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SomeProjectiveObject. \(F: ( arg2 ) \mapsto \mathtt{SomeProjectiveObject}(arg2)\).

7.7-222 AddSomeReductionBySplitEpiSummand
‣ AddSomeReductionBySplitEpiSummand( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SomeReductionBySplitEpiSummand. \(F: ( alpha ) \mapsto \mathtt{SomeReductionBySplitEpiSummand}(alpha)\).

7.7-223 AddSomeReductionBySplitEpiSummand_MorphismFromInputRange
‣ AddSomeReductionBySplitEpiSummand_MorphismFromInputRange( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SomeReductionBySplitEpiSummand_MorphismFromInputRange. \(F: ( alpha ) \mapsto \mathtt{SomeReductionBySplitEpiSummand_MorphismFromInputRange}(alpha)\).

7.7-224 AddSomeReductionBySplitEpiSummand_MorphismToInputRange
‣ AddSomeReductionBySplitEpiSummand_MorphismToInputRange( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SomeReductionBySplitEpiSummand_MorphismToInputRange. \(F: ( alpha ) \mapsto \mathtt{SomeReductionBySplitEpiSummand_MorphismToInputRange}(alpha)\).

7.7-225 AddSubtractionForMorphisms
‣ AddSubtractionForMorphisms( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation SubtractionForMorphisms. \(F: ( a, b ) \mapsto \mathtt{SubtractionForMorphisms}(a, b)\).

7.7-226 AddTerminalObject
‣ AddTerminalObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation TerminalObject. \(F: ( ) \mapsto \mathtt{TerminalObject}()\).

7.7-227 AddTerminalObjectFunctorial
‣ AddTerminalObjectFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation TerminalObjectFunctorial. \(F: ( ) \mapsto \mathtt{TerminalObjectFunctorial}()\).

7.7-228 AddTerminalObjectFunctorialWithGivenTerminalObjects
‣ AddTerminalObjectFunctorialWithGivenTerminalObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation TerminalObjectFunctorialWithGivenTerminalObjects. \(F: ( P, Pp ) \mapsto \mathtt{TerminalObjectFunctorialWithGivenTerminalObjects}(P, Pp)\).

7.7-229 AddUniversalMorphismFromCoequalizer
‣ AddUniversalMorphismFromCoequalizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromCoequalizer. \(F: ( morphisms, T, tau ) \mapsto \mathtt{UniversalMorphismFromCoequalizer}(morphisms, T, tau)\).

7.7-230 AddUniversalMorphismFromCoequalizerWithGivenCoequalizer
‣ AddUniversalMorphismFromCoequalizerWithGivenCoequalizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromCoequalizerWithGivenCoequalizer. \(F: ( morphisms, T, tau, P ) \mapsto \mathtt{UniversalMorphismFromCoequalizerWithGivenCoequalizer}(morphisms, T, tau, P)\).

7.7-231 AddUniversalMorphismFromCoproduct
‣ AddUniversalMorphismFromCoproduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromCoproduct. \(F: ( objects, T, tau ) \mapsto \mathtt{UniversalMorphismFromCoproduct}(objects, T, tau)\).

7.7-232 AddUniversalMorphismFromCoproductWithGivenCoproduct
‣ AddUniversalMorphismFromCoproductWithGivenCoproduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromCoproductWithGivenCoproduct. \(F: ( objects, T, tau, P ) \mapsto \mathtt{UniversalMorphismFromCoproductWithGivenCoproduct}(objects, T, tau, P)\).

7.7-233 AddUniversalMorphismFromDirectSum
‣ AddUniversalMorphismFromDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromDirectSum. \(F: ( objects, T, tau ) \mapsto \mathtt{UniversalMorphismFromDirectSum}(objects, T, tau)\).

7.7-234 AddUniversalMorphismFromDirectSumWithGivenDirectSum
‣ AddUniversalMorphismFromDirectSumWithGivenDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromDirectSumWithGivenDirectSum. \(F: ( objects, T, tau, P ) \mapsto \mathtt{UniversalMorphismFromDirectSumWithGivenDirectSum}(objects, T, tau, P)\).

7.7-235 AddUniversalMorphismFromImage
‣ AddUniversalMorphismFromImage( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromImage. \(F: ( alpha, tau ) \mapsto \mathtt{UniversalMorphismFromImage}(alpha, tau)\).

7.7-236 AddUniversalMorphismFromImageWithGivenImageObject
‣ AddUniversalMorphismFromImageWithGivenImageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromImageWithGivenImageObject. \(F: ( alpha, tau, I ) \mapsto \mathtt{UniversalMorphismFromImageWithGivenImageObject}(alpha, tau, I)\).

7.7-237 AddUniversalMorphismFromInitialObject
‣ AddUniversalMorphismFromInitialObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromInitialObject. \(F: ( T ) \mapsto \mathtt{UniversalMorphismFromInitialObject}(T)\).

7.7-238 AddUniversalMorphismFromInitialObjectWithGivenInitialObject
‣ AddUniversalMorphismFromInitialObjectWithGivenInitialObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromInitialObjectWithGivenInitialObject. \(F: ( T, P ) \mapsto \mathtt{UniversalMorphismFromInitialObjectWithGivenInitialObject}(T, P)\).

7.7-239 AddUniversalMorphismFromPushout
‣ AddUniversalMorphismFromPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromPushout. \(F: ( morphisms, T, tau ) \mapsto \mathtt{UniversalMorphismFromPushout}(morphisms, T, tau)\).

7.7-240 AddUniversalMorphismFromPushoutWithGivenPushout
‣ AddUniversalMorphismFromPushoutWithGivenPushout( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromPushoutWithGivenPushout. \(F: ( morphisms, T, tau, P ) \mapsto \mathtt{UniversalMorphismFromPushoutWithGivenPushout}(morphisms, T, tau, P)\).

7.7-241 AddUniversalMorphismFromZeroObject
‣ AddUniversalMorphismFromZeroObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromZeroObject. \(F: ( T ) \mapsto \mathtt{UniversalMorphismFromZeroObject}(T)\).

7.7-242 AddUniversalMorphismFromZeroObjectWithGivenZeroObject
‣ AddUniversalMorphismFromZeroObjectWithGivenZeroObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismFromZeroObjectWithGivenZeroObject. \(F: ( T, P ) \mapsto \mathtt{UniversalMorphismFromZeroObjectWithGivenZeroObject}(T, P)\).

7.7-243 AddUniversalMorphismIntoCoimage
‣ AddUniversalMorphismIntoCoimage( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoCoimage. \(F: ( alpha, tau ) \mapsto \mathtt{UniversalMorphismIntoCoimage}(alpha, tau)\).

7.7-244 AddUniversalMorphismIntoCoimageWithGivenCoimageObject
‣ AddUniversalMorphismIntoCoimageWithGivenCoimageObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoCoimageWithGivenCoimageObject. \(F: ( alpha, tau, C ) \mapsto \mathtt{UniversalMorphismIntoCoimageWithGivenCoimageObject}(alpha, tau, C)\).

7.7-245 AddUniversalMorphismIntoDirectProduct
‣ AddUniversalMorphismIntoDirectProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoDirectProduct. \(F: ( objects, T, tau ) \mapsto \mathtt{UniversalMorphismIntoDirectProduct}(objects, T, tau)\).

7.7-246 AddUniversalMorphismIntoDirectProductWithGivenDirectProduct
‣ AddUniversalMorphismIntoDirectProductWithGivenDirectProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoDirectProductWithGivenDirectProduct. \(F: ( objects, T, tau, P ) \mapsto \mathtt{UniversalMorphismIntoDirectProductWithGivenDirectProduct}(objects, T, tau, P)\).

7.7-247 AddUniversalMorphismIntoDirectSum
‣ AddUniversalMorphismIntoDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoDirectSum. \(F: ( objects, T, tau ) \mapsto \mathtt{UniversalMorphismIntoDirectSum}(objects, T, tau)\).

7.7-248 AddUniversalMorphismIntoDirectSumWithGivenDirectSum
‣ AddUniversalMorphismIntoDirectSumWithGivenDirectSum( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoDirectSumWithGivenDirectSum. \(F: ( objects, T, tau, P ) \mapsto \mathtt{UniversalMorphismIntoDirectSumWithGivenDirectSum}(objects, T, tau, P)\).

7.7-249 AddUniversalMorphismIntoEqualizer
‣ AddUniversalMorphismIntoEqualizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoEqualizer. \(F: ( morphisms, T, tau ) \mapsto \mathtt{UniversalMorphismIntoEqualizer}(morphisms, T, tau)\).

7.7-250 AddUniversalMorphismIntoEqualizerWithGivenEqualizer
‣ AddUniversalMorphismIntoEqualizerWithGivenEqualizer( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoEqualizerWithGivenEqualizer. \(F: ( morphisms, T, tau, P ) \mapsto \mathtt{UniversalMorphismIntoEqualizerWithGivenEqualizer}(morphisms, T, tau, P)\).

7.7-251 AddUniversalMorphismIntoFiberProduct
‣ AddUniversalMorphismIntoFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoFiberProduct. \(F: ( morphisms, T, tau ) \mapsto \mathtt{UniversalMorphismIntoFiberProduct}(morphisms, T, tau)\).

7.7-252 AddUniversalMorphismIntoFiberProductWithGivenFiberProduct
‣ AddUniversalMorphismIntoFiberProductWithGivenFiberProduct( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoFiberProductWithGivenFiberProduct. \(F: ( morphisms, T, tau, P ) \mapsto \mathtt{UniversalMorphismIntoFiberProductWithGivenFiberProduct}(morphisms, T, tau, P)\).

7.7-253 AddUniversalMorphismIntoTerminalObject
‣ AddUniversalMorphismIntoTerminalObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoTerminalObject. \(F: ( T ) \mapsto \mathtt{UniversalMorphismIntoTerminalObject}(T)\).

7.7-254 AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject
‣ AddUniversalMorphismIntoTerminalObjectWithGivenTerminalObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoTerminalObjectWithGivenTerminalObject. \(F: ( T, P ) \mapsto \mathtt{UniversalMorphismIntoTerminalObjectWithGivenTerminalObject}(T, P)\).

7.7-255 AddUniversalMorphismIntoZeroObject
‣ AddUniversalMorphismIntoZeroObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoZeroObject. \(F: ( T ) \mapsto \mathtt{UniversalMorphismIntoZeroObject}(T)\).

7.7-256 AddUniversalMorphismIntoZeroObjectWithGivenZeroObject
‣ AddUniversalMorphismIntoZeroObjectWithGivenZeroObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniversalMorphismIntoZeroObjectWithGivenZeroObject. \(F: ( T, P ) \mapsto \mathtt{UniversalMorphismIntoZeroObjectWithGivenZeroObject}(T, P)\).

7.7-257 AddVerticalPostCompose
‣ AddVerticalPostCompose( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation VerticalPostCompose. \(F: ( arg2, arg3 ) \mapsto \mathtt{VerticalPostCompose}(arg2, arg3)\).

7.7-258 AddVerticalPreCompose
‣ AddVerticalPreCompose( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation VerticalPreCompose. \(F: ( arg2, arg3 ) \mapsto \mathtt{VerticalPreCompose}(arg2, arg3)\).

7.7-259 AddZeroMorphism
‣ AddZeroMorphism( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ZeroMorphism. \(F: ( a, b ) \mapsto \mathtt{ZeroMorphism}(a, b)\).

7.7-260 AddZeroObject
‣ AddZeroObject( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ZeroObject. \(F: ( ) \mapsto \mathtt{ZeroObject}()\).

7.7-261 AddZeroObjectFunctorial
‣ AddZeroObjectFunctorial( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ZeroObjectFunctorial. \(F: ( ) \mapsto \mathtt{ZeroObjectFunctorial}()\).

7.7-262 AddZeroObjectFunctorialWithGivenZeroObjects
‣ AddZeroObjectFunctorialWithGivenZeroObjects( C, F )( operation )

Returns: nothing

The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation ZeroObjectFunctorialWithGivenZeroObjects. \(F: ( P, Pp ) \mapsto \mathtt{ZeroObjectFunctorialWithGivenZeroObjects}(P, Pp)\).

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