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# SPDX-License-Identifier: GPL-2.0-or-later
# CAP: Categories, Algorithms, Programming
#
# Declarations
#
# THIS FILE IS AUTOMATICALLY GENERATED, SEE CAP_project/CAP/gap/MethodRecordTools.gi
#! @Chapter Add Functions
#! @Section Available Add functions
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, beta ) \mapsto \mathtt{AdditionForMorphisms}(alpha, beta)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddAdditionForMorphisms",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddAdditionForMorphisms",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( ) \mapsto \mathtt{AdditiveGenerators}()$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddAdditiveGenerators",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddAdditiveGenerators",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{AdditiveInverseForMorphisms}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddAdditiveInverseForMorphisms",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddAdditiveInverseForMorphisms",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{AstrictionToCoimage}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddAstrictionToCoimage",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddAstrictionToCoimage",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, C ) \mapsto \mathtt{AstrictionToCoimageWithGivenCoimageObject}(alpha, C)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddAstrictionToCoimageWithGivenCoimageObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddAstrictionToCoimageWithGivenCoimageObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2, arg3 ) \mapsto \mathtt{BasisOfExternalHom}(arg2, arg3)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddBasisOfExternalHom",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddBasisOfExternalHom",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `BasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2, arg3, arg4, arg5 ) \mapsto \mathtt{BasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory}(arg2, arg3, arg4, arg5)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddBasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddBasisOfSolutionsOfHomogeneousDoubleLinearSystemInLinearCategory",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `BasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2, arg3 ) \mapsto \mathtt{BasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory}(arg2, arg3)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddBasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddBasisOfSolutionsOfHomogeneousLinearSystemInLinearCategory",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{CoastrictionToImage}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoastrictionToImage",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoastrictionToImage",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, I ) \mapsto \mathtt{CoastrictionToImageWithGivenImageObject}(alpha, I)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoastrictionToImageWithGivenImageObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoastrictionToImageWithGivenImageObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `CoefficientsOfMorphism`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2 ) \mapsto \mathtt{CoefficientsOfMorphism}(arg2)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoefficientsOfMorphism",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoefficientsOfMorphism",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( Y, morphisms ) \mapsto \mathtt{Coequalizer}(Y, morphisms)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoequalizer",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoequalizer",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( morphisms, mu, morphismsp ) \mapsto \mathtt{CoequalizerFunctorial}(morphisms, mu, morphismsp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoequalizerFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoequalizerFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, morphisms, mu, morphismsp, Pp ) \mapsto \mathtt{CoequalizerFunctorialWithGivenCoequalizers}(P, morphisms, mu, morphismsp, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoequalizerFunctorialWithGivenCoequalizers",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoequalizerFunctorialWithGivenCoequalizers",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2 ) \mapsto \mathtt{CoimageObject}(arg2)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoimageObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoimageObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `CoimageObjectFunctorial`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, mu, alphap ) \mapsto \mathtt{CoimageObjectFunctorial}(alpha, mu, alphap)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoimageObjectFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoimageObjectFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `CoimageObjectFunctorialWithGivenCoimageObjects`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( C, alpha, mu, alphap, Cp ) \mapsto \mathtt{CoimageObjectFunctorialWithGivenCoimageObjects}(C, alpha, mu, alphap, Cp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoimageObjectFunctorialWithGivenCoimageObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoimageObjectFunctorialWithGivenCoimageObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{CoimageProjection}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoimageProjection",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoimageProjection",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, C ) \mapsto \mathtt{CoimageProjectionWithGivenCoimageObject}(alpha, C)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoimageProjectionWithGivenCoimageObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoimageProjectionWithGivenCoimageObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, T, tau ) \mapsto \mathtt{CokernelColift}(alpha, T, tau)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCokernelColift",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCokernelColift",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, T, tau, P ) \mapsto \mathtt{CokernelColiftWithGivenCokernelObject}(alpha, T, tau, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCokernelColiftWithGivenCokernelObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCokernelColiftWithGivenCokernelObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{CokernelObject}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCokernelObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCokernelObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, mu, alphap ) \mapsto \mathtt{CokernelObjectFunctorial}(alpha, mu, alphap)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCokernelObjectFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCokernelObjectFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, alpha, mu, alphap, Pp ) \mapsto \mathtt{CokernelObjectFunctorialWithGivenCokernelObjects}(P, alpha, mu, alphap, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCokernelObjectFunctorialWithGivenCokernelObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCokernelObjectFunctorialWithGivenCokernelObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{CokernelProjection}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCokernelProjection",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCokernelProjection",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, P ) \mapsto \mathtt{CokernelProjectionWithGivenCokernelObject}(alpha, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCokernelProjectionWithGivenCokernelObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCokernelProjectionWithGivenCokernelObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, beta ) \mapsto \mathtt{Colift}(alpha, beta)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddColift",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddColift",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( epsilon, tau ) \mapsto \mathtt{ColiftAlongEpimorphism}(epsilon, tau)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddColiftAlongEpimorphism",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddColiftAlongEpimorphism",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `ComponentOfMorphismFromCoproduct`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, I, i ) \mapsto \mathtt{ComponentOfMorphismFromCoproduct}(alpha, I, i)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddComponentOfMorphismFromCoproduct",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddComponentOfMorphismFromCoproduct",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, S, i ) \mapsto \mathtt{ComponentOfMorphismFromDirectSum}(alpha, S, i)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddComponentOfMorphismFromDirectSum",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddComponentOfMorphismFromDirectSum",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `ComponentOfMorphismIntoDirectProduct`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, P, i ) \mapsto \mathtt{ComponentOfMorphismIntoDirectProduct}(alpha, P, i)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddComponentOfMorphismIntoDirectProduct",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddComponentOfMorphismIntoDirectProduct",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, S, i ) \mapsto \mathtt{ComponentOfMorphismIntoDirectSum}(alpha, S, i)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddComponentOfMorphismIntoDirectSum",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddComponentOfMorphismIntoDirectSum",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects ) \mapsto \mathtt{Coproduct}(objects)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoproduct",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoproduct",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects, L, objectsp ) \mapsto \mathtt{CoproductFunctorial}(objects, L, objectsp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoproductFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoproductFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, objects, L, objectsp, Pp ) \mapsto \mathtt{CoproductFunctorialWithGivenCoproducts}(P, objects, L, objectsp, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddCoproductFunctorialWithGivenCoproducts",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddCoproductFunctorialWithGivenCoproducts",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects ) \mapsto \mathtt{DirectProduct}(objects)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddDirectProduct",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddDirectProduct",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects, L, objectsp ) \mapsto \mathtt{DirectProductFunctorial}(objects, L, objectsp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddDirectProductFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddDirectProductFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, objects, L, objectsp, Pp ) \mapsto \mathtt{DirectProductFunctorialWithGivenDirectProducts}(P, objects, L, objectsp, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddDirectProductFunctorialWithGivenDirectProducts",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddDirectProductFunctorialWithGivenDirectProducts",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects ) \mapsto \mathtt{DirectSum}(objects)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddDirectSum",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddDirectSum",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects, L, objectsp ) \mapsto \mathtt{DirectSumFunctorial}(objects, L, objectsp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddDirectSumFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddDirectSumFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, objects, L, objectsp, Pp ) \mapsto \mathtt{DirectSumFunctorialWithGivenDirectSums}(P, objects, L, objectsp, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddDirectSumFunctorialWithGivenDirectSums",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddDirectSumFunctorialWithGivenDirectSums",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( ) \mapsto \mathtt{DistinguishedObjectOfHomomorphismStructure}()$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddDistinguishedObjectOfHomomorphismStructure",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddDistinguishedObjectOfHomomorphismStructure",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( Y, morphisms ) \mapsto \mathtt{EmbeddingOfEqualizer}(Y, morphisms)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEmbeddingOfEqualizer",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEmbeddingOfEqualizer",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( Y, morphisms, P ) \mapsto \mathtt{EmbeddingOfEqualizerWithGivenEqualizer}(Y, morphisms, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEmbeddingOfEqualizerWithGivenEqualizer",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEmbeddingOfEqualizerWithGivenEqualizer",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `EpimorphismFromProjectiveCoverObject`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( A ) \mapsto \mathtt{EpimorphismFromProjectiveCoverObject}(A)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEpimorphismFromProjectiveCoverObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEpimorphismFromProjectiveCoverObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `EpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( A, P ) \mapsto \mathtt{EpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject}(A, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEpimorphismFromProjectiveCoverObjectWithGivenProjectiveCoverObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( A ) \mapsto \mathtt{EpimorphismFromSomeProjectiveObject}(A)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEpimorphismFromSomeProjectiveObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEpimorphismFromSomeProjectiveObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( A, P ) \mapsto \mathtt{EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject}(A, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( Y, morphisms ) \mapsto \mathtt{Equalizer}(Y, morphisms)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEqualizer",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEqualizer",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( morphisms, mu, morphismsp ) \mapsto \mathtt{EqualizerFunctorial}(morphisms, mu, morphismsp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEqualizerFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEqualizerFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, morphisms, mu, morphismsp, Pp ) \mapsto \mathtt{EqualizerFunctorialWithGivenEqualizers}(P, morphisms, mu, morphismsp, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddEqualizerFunctorialWithGivenEqualizers",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddEqualizerFunctorialWithGivenEqualizers",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( morphisms ) \mapsto \mathtt{FiberProduct}(morphisms)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddFiberProduct",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddFiberProduct",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( morphisms, L, morphismsp ) \mapsto \mathtt{FiberProductFunctorial}(morphisms, L, morphismsp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddFiberProductFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddFiberProductFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, morphisms, L, morphismsp, Pp ) \mapsto \mathtt{FiberProductFunctorialWithGivenFiberProducts}(P, morphisms, L, morphismsp, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddFiberProductFunctorialWithGivenFiberProducts",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddFiberProductFunctorialWithGivenFiberProducts",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, beta ) \mapsto \mathtt{HomologyObject}(alpha, beta)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddHomologyObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddHomologyObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( H_1, L, H_2 ) \mapsto \mathtt{HomologyObjectFunctorialWithGivenHomologyObjects}(H_1, L, H_2)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddHomologyObjectFunctorialWithGivenHomologyObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddHomologyObjectFunctorialWithGivenHomologyObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, beta ) \mapsto \mathtt{HomomorphismStructureOnMorphisms}(alpha, beta)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddHomomorphismStructureOnMorphisms",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddHomomorphismStructureOnMorphisms",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( source, alpha, beta, range ) \mapsto \mathtt{HomomorphismStructureOnMorphismsWithGivenObjects}(source, alpha, beta, range)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddHomomorphismStructureOnMorphismsWithGivenObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddHomomorphismStructureOnMorphismsWithGivenObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2, arg3 ) \mapsto \mathtt{HomomorphismStructureOnObjects}(arg2, arg3)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddHomomorphismStructureOnObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddHomomorphismStructureOnObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2, arg3 ) \mapsto \mathtt{HorizontalPostCompose}(arg2, arg3)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddHorizontalPostCompose",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddHorizontalPostCompose",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2, arg3 ) \mapsto \mathtt{HorizontalPreCompose}(arg2, arg3)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddHorizontalPreCompose",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddHorizontalPreCompose",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( a ) \mapsto \mathtt{IdentityMorphism}(a)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddIdentityMorphism",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddIdentityMorphism",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2 ) \mapsto \mathtt{IdentityTwoCell}(arg2)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddIdentityTwoCell",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddIdentityTwoCell",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{ImageEmbedding}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddImageEmbedding",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddImageEmbedding",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, I ) \mapsto \mathtt{ImageEmbeddingWithGivenImageObject}(alpha, I)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddImageEmbeddingWithGivenImageObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddImageEmbeddingWithGivenImageObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2 ) \mapsto \mathtt{ImageObject}(arg2)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddImageObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddImageObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `ImageObjectFunctorial`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, nu, alphap ) \mapsto \mathtt{ImageObjectFunctorial}(alpha, nu, alphap)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddImageObjectFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddImageObjectFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `ImageObjectFunctorialWithGivenImageObjects`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( I, alpha, nu, alphap, Ip ) \mapsto \mathtt{ImageObjectFunctorialWithGivenImageObjects}(I, alpha, nu, alphap, Ip)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddImageObjectFunctorialWithGivenImageObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddImageObjectFunctorialWithGivenImageObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `IndecomposableInjectiveObjects`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( ) \mapsto \mathtt{IndecomposableInjectiveObjects}()$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddIndecomposableInjectiveObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddIndecomposableInjectiveObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `IndecomposableProjectiveObjects`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( ) \mapsto \mathtt{IndecomposableProjectiveObjects}()$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddIndecomposableProjectiveObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddIndecomposableProjectiveObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( ) \mapsto \mathtt{InitialObject}()$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInitialObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInitialObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( ) \mapsto \mathtt{InitialObjectFunctorial}()$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInitialObjectFunctorial",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInitialObjectFunctorial",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( P, Pp ) \mapsto \mathtt{InitialObjectFunctorialWithGivenInitialObjects}(P, Pp)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInitialObjectFunctorialWithGivenInitialObjects",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInitialObjectFunctorialWithGivenInitialObjects",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects, k ) \mapsto \mathtt{InjectionOfCofactorOfCoproduct}(objects, k)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectionOfCofactorOfCoproduct",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectionOfCofactorOfCoproduct",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects, k, P ) \mapsto \mathtt{InjectionOfCofactorOfCoproductWithGivenCoproduct}(objects, k, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectionOfCofactorOfCoproductWithGivenCoproduct",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectionOfCofactorOfCoproductWithGivenCoproduct",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects, k ) \mapsto \mathtt{InjectionOfCofactorOfDirectSum}(objects, k)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectionOfCofactorOfDirectSum",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectionOfCofactorOfDirectSum",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( objects, k, P ) \mapsto \mathtt{InjectionOfCofactorOfDirectSumWithGivenDirectSum}(objects, k, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectionOfCofactorOfDirectSumWithGivenDirectSum",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectionOfCofactorOfDirectSumWithGivenDirectSum",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( morphisms, k ) \mapsto \mathtt{InjectionOfCofactorOfPushout}(morphisms, k)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectionOfCofactorOfPushout",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectionOfCofactorOfPushout",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( morphisms, k, P ) \mapsto \mathtt{InjectionOfCofactorOfPushoutWithGivenPushout}(morphisms, k, P)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectionOfCofactorOfPushoutWithGivenPushout",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectionOfCofactorOfPushoutWithGivenPushout",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha, beta ) \mapsto \mathtt{InjectiveColift}(alpha, beta)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectiveColift",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectiveColift",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2 ) \mapsto \mathtt{InjectiveDimension}(arg2)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectiveDimension",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectiveDimension",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
#! to the category for the basic operation `InjectiveEnvelopeObject`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( arg2 ) \mapsto \mathtt{InjectiveEnvelopeObject}(arg2)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInjectiveEnvelopeObject",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInjectiveEnvelopeObject",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! 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`.
#! Optionally, a weight (default: 100) can be specified which should roughly correspond
#! to the computational complexity of the function (lower weight = less complex = faster execution).
#! $F: ( alpha ) \mapsto \mathtt{InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure}(alpha)$.
#! @Returns nothing
#! @Arguments C, F
DeclareOperation( "AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure",
[ IsCapCategory, IsFunction ] );
#! @Arguments C, F, weight
DeclareOperation( "AddInterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure",
[ IsCapCategory, IsFunction, IsInt ] );
#! @EndGroup
#! @BeginGroup
#! @Description
#! The arguments are a category $C$ and a function $F$.
#! This operation adds the given function $F$
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