‣ LeftPresentationWithDegrees ( mat ) | ( operation ) |
Returns: a homalg graded left module
This constructor returns the finitely presented left module with homogeneous relations given by the rows of the homalg matrix mat.
‣ RightPresentationWithDegrees ( mat ) | ( operation ) |
Returns: a homalg graded right module
This constructor returns the finitely presented right module with homogeneous relations given by the columns of the homalg matrix mat.
‣ CategoryOfHomalgFinitelyPresentedGradedLeftModules ( R ) | ( attribute ) |
Returns: an intrinsic cateogry of left modules
Construct the category of finitely presented graded left modules over the computable graded ring S.
‣ CategoryOfHomalgFinitelyPresentedGradedRightModules ( R ) | ( attribute ) |
Returns: an intrinsic cateogry of right modules
Construct the category of finitely presented graded right modules over the computable graded ring S.
‣ FunctorStandardGradedModuleLeft ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S. The output is a functor which takes a graded left presentation as input and computes its standard presentation.
‣ FunctorStandardGradedModuleRight ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S. The output is a functor which takes a graded right presentation as input and computes its standard presentation.
‣ FunctorGetRidOfZeroHomogeneousGeneratorsLeft ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S. The output is a functor which takes a graded left presentation as input and gets rid of the zero generators.
‣ FunctorGetRidOfZeroHomogeneousGeneratorsRight ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S. The output is a functor which takes a graded right presentation as input and gets rid of the zero generators.
‣ FunctorLessHomogeneousGeneratorsLeft ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S. The output is functor which takes a graded left presentation as input and computes a presentation having less generators.
‣ FunctorLessHomogeneousGeneratorsRight ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S. The output is functor which takes a graded right presentation as input and computes a presentation having less generators.
‣ FunctorGradedDualLeft ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S that has an involution function. The output is functor which takes a graded left presentation M as input and computes its Hom(M, R) as a graded left presentation.
‣ FunctorGradedDualRight ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S that has an involution function. The output is functor which takes a graded right presentation M as input and computes its Hom(M, R) as a graded right presentation.
‣ FunctorDoubleGradedDualLeft ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S that has an involution function. The output is functor which takes a graded left presentation M as input and computes its Hom( Hom(M, R), R ) as a graded left presentation.
‣ FunctorDoubleGradedDualRight ( S ) | ( attribute ) |
Returns: a functor
The argument is a homalg graded ring S that has an involution function. The output is functor which takes a graded right presentation M as input and computes its Hom( Hom(M, R), R ) as a graded right presentation.
‣ NaturalIsomorphismFromIdentityToStandardGradedModuleLeft ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{StandardGradedModuleLeft}
The argument is a homalg graded ring S. The output is the natural isomorphism from the identity functor to the left standard module functor.
‣ NaturalIsomorphismFromIdentityToStandardGradedModuleRight ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{StandardGradedModuleRight}
The argument is a homalg graded ring S. The output is the natural isomorphism from the identity functor to the right standard module functor.
‣ NaturalIsomorphismFromIdentityToGetRidOfZeroHomogeneousGeneratorsLeft ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{GetRidOfZeroHomogeneousGeneratorsLeft}
The argument is a homalg graded ring S. The output is the natural isomorphism from the identity functor to the functor that gets rid of zero generators of left modules.
‣ NaturalIsomorphismFromIdentityToGetRidOfZeroHomogeneousGeneratorsRight ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{GetRidOfZeroHomogeneousGeneratorsRight}
The argument is a homalg graded ring S. The output is the natural isomorphism from the identity functor to the functor that gets rid of zero generators of right modules.
‣ NaturalIsomorphismFromIdentityToLessHomogeneousGeneratorsLeft ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{LessHomogeneousGeneratorsLeft}
The argument is a homalg graded ring S. The output is the natural morphism from the identity functor to the left less generators functor.
‣ NaturalIsomorphismFromIdentityToLessHomogeneousGeneratorsRight ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{LessHomogeneousGeneratorsRight}
The argument is a homalg graded ring S. The output is the natural morphism from the identity functor to the right less generator functor.
‣ NaturalTransformationFromIdentityToDoubleGradedDualLeft ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{FunctorDoubleGradedDualLeft}
The argument is a homalg graded ring S. The output is the natural morphism from the identity functor to the double dual functor in left Presentations category.
‣ NaturalTransformationFromIdentityToDoubleGradedDualRight ( S ) | ( attribute ) |
Returns: a natural transformation \mathrm{Id} \rightarrow \mathrm{FunctorDoubleGradedDualRight}
The argument is a homalg graded ring S. The output is the natural morphism from the identity functor to the double dual functor in right Presentations category.
gap> Q := GradedRing( HomalgFieldOfRationalsInSingular( ) ); Q (weights: yet unset) gap> S := Q["x,y,z"]; Q[x,y,z] (weights: yet unset) gap> A := CategoryOfHomalgFinitelyPresentedGradedLeftModules( S ); IntrinsicCategory( CategoryWithAmbientObjects( Freyd( GradedRows( Q[x,y,z] (with weights [ 1, 1, 1 ]) ) ) ) ) gap> Display( A ); A CAP category with name IntrinsicCategory( CategoryWithAmbientObjects( Freyd( GradedRows( Q[x,y,z] (with weights [ 1, 1, 1 ]) ) ) ) ): 184 primitive operations were used to derive 376 operations for this category which algorithmically * IsEquippedWithHomomorphismStructure * IsSymmetricClosedMonoidalCategory * IsAbelianCategoryWithEnoughProjectives gap> mat := HomalgMatrix( "[ 0, z, -y, -z, 0, x, y, -x, 0 ]", 3, 3, S ); <A 3 x 3 matrix over a graded ring> gap> phi := GradedMap( mat, "left", S ); <A homomorphism of left graded modules> gap> IsWellDefined( phi ); true gap> phi; <A homomorphism of left graded modules> gap> N := CokernelObject( phi ); <A graded left module presented by 3 relations for 3 generators> gap> Display( N ); 0, z, -y, -z,0, x, y, -x,0 (over a graded ring) Cokernel of the map R^(1x3) --> R^(1x3), ( for R := Q[x,y,z] (with weights [ 1, 1, 1 ]) ) currently represented by the above matrix (graded, degrees of generators: [ 0, 0, 0 ]) gap> H := InternalHomOnObjects( N, N ); <A graded left module presented by 2 relations for 3 generators> gap> M := LeftPresentationWithDegrees( mat ); <A graded left module presented by 3 relations for 3 generators> gap> IsWellDefined( M ); true gap> 1 * S; <The graded free left module of rank 1 on a free generator> gap> 0 * S; <A graded zero left module> gap> ZeroObject( A ); <A graded zero left module> gap> 0 * S = ZeroObject( A ); true gap> Ms := DualOnObjects( M ); <A graded free left module of rank 1 on a free generator> gap> Display( Ms ); Q[x,y,z] (with weights [ 1, 1, 1 ])^(1 x 1) (graded, degree of generator: 1) gap> pi := EpimorphismFromSomeProjectiveObject( M ); <A homomorphism of left graded modules> gap> IsWellDefined( pi ); true gap> Display( pi ); 1,0,0, 0,1,0, 0,0,1 (over a graded ring) the graded map is currently represented by the above 3 x 3 matrix (degrees of generators of target: [ 0, 0, 0 ])
The following CAP operations are supported:
AdditionForMorphisms
(CAP: AdditionForMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
AdditiveInverseForMorphisms
(CAP: AdditiveInverseForMorphisms for IsCapCategoryMorphism)
AssociatorLeftToRight
(MonoidalCategories: AssociatorLeftToRight for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
AssociatorLeftToRightWithGivenTensorProducts
(MonoidalCategories: AssociatorLeftToRightWithGivenTensorProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
AssociatorRightToLeft
(MonoidalCategories: AssociatorRightToLeft for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
AssociatorRightToLeftWithGivenTensorProducts
(MonoidalCategories: AssociatorRightToLeftWithGivenTensorProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
AstrictionToCoimage
(CAP: AstrictionToCoimage for IsCapCategoryMorphism)
AstrictionToCoimageWithGivenCoimageObject
(CAP: AstrictionToCoimageWithGivenCoimageObject for IsCapCategoryMorphism, IsCapCategoryObject)
BiasedWeakFiberProduct
(FreydCategoriesForCAP: BiasedWeakFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism)
BiasedWeakPushout
(FreydCategoriesForCAP: BiasedWeakPushout for IsCapCategoryMorphism, IsCapCategoryMorphism)
Braiding
(MonoidalCategories: Braiding for IsCapCategoryObject, IsCapCategoryObject)
BraidingInverse
(MonoidalCategories: BraidingInverse for IsCapCategoryObject, IsCapCategoryObject)
BraidingInverseWithGivenTensorProducts
(MonoidalCategories: BraidingInverseWithGivenTensorProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
BraidingWithGivenTensorProducts
(MonoidalCategories: BraidingWithGivenTensorProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CartesianAssociatorLeftToRight
(CartesianCategories: CartesianAssociatorLeftToRight for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CartesianAssociatorLeftToRightWithGivenDirectProducts
(CartesianCategories: CartesianAssociatorLeftToRightWithGivenDirectProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CartesianAssociatorRightToLeft
(CartesianCategories: CartesianAssociatorRightToLeft for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CartesianAssociatorRightToLeftWithGivenDirectProducts
(CartesianCategories: CartesianAssociatorRightToLeftWithGivenDirectProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CartesianBraiding
(CartesianCategories: CartesianBraiding for IsCapCategoryObject, IsCapCategoryObject)
CartesianBraidingInverse
(CartesianCategories: CartesianBraidingInverse for IsCapCategoryObject, IsCapCategoryObject)
CartesianBraidingInverseWithGivenDirectProducts
(CartesianCategories: CartesianBraidingInverseWithGivenDirectProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CartesianBraidingWithGivenDirectProducts
(CartesianCategories: CartesianBraidingWithGivenDirectProducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CartesianDiagonal
(CartesianCategories: CartesianDiagonal for IsCapCategoryObject, IsInt)
CartesianDiagonalWithGivenCartesianPower
(CartesianCategories: CartesianDiagonalWithGivenCartesianPower for IsCapCategoryObject, IsInt, IsCapCategoryObject)
CartesianLeftUnitor
(CartesianCategories: CartesianLeftUnitor for IsCapCategoryObject)
CartesianLeftUnitorInverse
(CartesianCategories: CartesianLeftUnitorInverse for IsCapCategoryObject)
CartesianLeftUnitorInverseWithGivenDirectProduct
(CartesianCategories: CartesianLeftUnitorInverseWithGivenDirectProduct for IsCapCategoryObject, IsCapCategoryObject)
CartesianLeftUnitorWithGivenDirectProduct
(CartesianCategories: CartesianLeftUnitorWithGivenDirectProduct for IsCapCategoryObject, IsCapCategoryObject)
CartesianRightUnitor
(CartesianCategories: CartesianRightUnitor for IsCapCategoryObject)
CartesianRightUnitorInverse
(CartesianCategories: CartesianRightUnitorInverse for IsCapCategoryObject)
CartesianRightUnitorInverseWithGivenDirectProduct
(CartesianCategories: CartesianRightUnitorInverseWithGivenDirectProduct for IsCapCategoryObject, IsCapCategoryObject)
CartesianRightUnitorWithGivenDirectProduct
(CartesianCategories: CartesianRightUnitorWithGivenDirectProduct for IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalLeftCoevaluationMorphism
(MonoidalCategories: ClosedMonoidalLeftCoevaluationMorphism for IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalLeftCoevaluationMorphismWithGivenRange
(MonoidalCategories: ClosedMonoidalLeftCoevaluationMorphismWithGivenRange for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalLeftEvaluationMorphism
(MonoidalCategories: ClosedMonoidalLeftEvaluationMorphism for IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalLeftEvaluationMorphismWithGivenSource
(MonoidalCategories: ClosedMonoidalLeftEvaluationMorphismWithGivenSource for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalRightCoevaluationMorphism
(MonoidalCategories: ClosedMonoidalRightCoevaluationMorphism for IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalRightCoevaluationMorphismWithGivenRange
(MonoidalCategories: ClosedMonoidalRightCoevaluationMorphismWithGivenRange for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalRightEvaluationMorphism
(MonoidalCategories: ClosedMonoidalRightEvaluationMorphism for IsCapCategoryObject, IsCapCategoryObject)
ClosedMonoidalRightEvaluationMorphismWithGivenSource
(MonoidalCategories: ClosedMonoidalRightEvaluationMorphismWithGivenSource for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CoastrictionToImage
(CAP: CoastrictionToImage for IsCapCategoryMorphism)
CoastrictionToImageWithGivenImageObject
(CAP: CoastrictionToImageWithGivenImageObject for IsCapCategoryMorphism, IsCapCategoryObject)
CocartesianAssociatorLeftToRight
(CartesianCategories: CocartesianAssociatorLeftToRight for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CocartesianAssociatorLeftToRightWithGivenCoproducts
(CartesianCategories: CocartesianAssociatorLeftToRightWithGivenCoproducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CocartesianAssociatorRightToLeft
(CartesianCategories: CocartesianAssociatorRightToLeft for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CocartesianAssociatorRightToLeftWithGivenCoproducts
(CartesianCategories: CocartesianAssociatorRightToLeftWithGivenCoproducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CocartesianBraiding
(CartesianCategories: CocartesianBraiding for IsCapCategoryObject, IsCapCategoryObject)
CocartesianBraidingInverse
(CartesianCategories: CocartesianBraidingInverse for IsCapCategoryObject, IsCapCategoryObject)
CocartesianBraidingInverseWithGivenCoproducts
(CartesianCategories: CocartesianBraidingInverseWithGivenCoproducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CocartesianBraidingWithGivenCoproducts
(CartesianCategories: CocartesianBraidingWithGivenCoproducts for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
CocartesianCodiagonal
(CartesianCategories: CocartesianCodiagonal for IsCapCategoryObject, IsInt)
CocartesianCodiagonalWithGivenCocartesianMultiple
(CartesianCategories: CocartesianCodiagonalWithGivenCocartesianMultiple for IsCapCategoryObject, IsInt, IsCapCategoryObject)
CocartesianLeftUnitor
(CartesianCategories: CocartesianLeftUnitor for IsCapCategoryObject)
CocartesianLeftUnitorInverse
(CartesianCategories: CocartesianLeftUnitorInverse for IsCapCategoryObject)
CocartesianLeftUnitorInverseWithGivenCoproduct
(CartesianCategories: CocartesianLeftUnitorInverseWithGivenCoproduct for IsCapCategoryObject, IsCapCategoryObject)
CocartesianLeftUnitorWithGivenCoproduct
(CartesianCategories: CocartesianLeftUnitorWithGivenCoproduct for IsCapCategoryObject, IsCapCategoryObject)
CocartesianRightUnitor
(CartesianCategories: CocartesianRightUnitor for IsCapCategoryObject)
CocartesianRightUnitorInverse
(CartesianCategories: CocartesianRightUnitorInverse for IsCapCategoryObject)
CocartesianRightUnitorInverseWithGivenCoproduct
(CartesianCategories: CocartesianRightUnitorInverseWithGivenCoproduct for IsCapCategoryObject, IsCapCategoryObject)
CocartesianRightUnitorWithGivenCoproduct
(CartesianCategories: CocartesianRightUnitorWithGivenCoproduct for IsCapCategoryObject, IsCapCategoryObject)
Coequalizer
(CAP: Coequalizer)
CoequalizerFunctorial
(CAP: CoequalizerFunctorial for IsList, IsCapCategoryMorphism, IsList)
CoequalizerFunctorialWithGivenCoequalizers
(CAP: CoequalizerFunctorialWithGivenCoequalizers for IsCapCategoryObject, IsList, IsCapCategoryMorphism, IsList, IsCapCategoryObject)
CoimageObject
(CAP: CoimageObject for IsCapCategoryMorphism)
CoimageObjectFunctorial
(CAP: CoimageObjectFunctorial for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism)
CoimageObjectFunctorialWithGivenCoimageObjects
(CAP: CoimageObjectFunctorialWithGivenCoimageObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
CoimageProjection
(CAP: CoimageProjection for IsCapCategoryMorphism)
CoimageProjectionWithGivenCoimageObject
(CAP: CoimageProjectionWithGivenCoimageObject for IsCapCategoryMorphism, IsCapCategoryObject)
CokernelColift
(CAP: CokernelColift for IsCapCategoryMorphism, IsCapCategoryObject, IsCapCategoryMorphism)
CokernelColiftWithGivenCokernelObject
(CAP: CokernelColiftWithGivenCokernelObject for IsCapCategoryMorphism, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
CokernelObject
(CAP: CokernelObject for IsCapCategoryMorphism)
CokernelObjectFunctorial
(CAP: CokernelObjectFunctorial for IsList)
CokernelObjectFunctorialWithGivenCokernelObjects
(CAP: CokernelObjectFunctorialWithGivenCokernelObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism,IsCapCategoryMorphism, IsCapCategoryObject)
CokernelProjection
(CAP: CokernelProjection for IsCapCategoryMorphism)
CokernelProjectionWithGivenCokernelObject
(CAP: CokernelProjectionWithGivenCokernelObject for IsCapCategoryMorphism, IsCapCategoryObject)
Colift
(CAP: Colift for IsCapCategoryMorphism, IsCapCategoryMorphism)
ColiftAlongEpimorphism
(CAP: ColiftAlongEpimorphism for IsCapCategoryMorphism, IsCapCategoryMorphism)
Colimit
(ToolsForCategoricalTowers: Colimit for IsList, IsList)
ComponentOfMorphismFromCoproduct
(CAP: ComponentOfMorphismFromCoproduct for IsCapCategoryMorphism, IsList, IsInt)
ComponentOfMorphismFromDirectSum
(CAP: ComponentOfMorphismFromDirectSum for IsCapCategoryMorphism, IsList, IsInt)
ComponentOfMorphismIntoDirectProduct
(CAP: ComponentOfMorphismIntoDirectProduct for IsCapCategoryMorphism, IsList, IsInt)
ComponentOfMorphismIntoDirectSum
(CAP: ComponentOfMorphismIntoDirectSum for IsCapCategoryMorphism, IsList, IsInt)
Coproduct
(CAP: Coproduct for IsList)
CoproductFunctorial
(CAP: CoproductFunctorial for IsList, IsList, IsList)
CoproductFunctorialWithGivenCoproducts
(CAP: CoproductFunctorialWithGivenCoproducts for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
CoproductOnMorphisms
(CartesianCategories: CoproductOnMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
CoproductOnMorphismsWithGivenCoproducts
(CartesianCategories: CoproductOnMorphismsWithGivenCoproducts for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
DirectProduct
(CAP: DirectProduct)
DirectProductFunctorial
(CAP: DirectProductFunctorial for IsList, IsList, IsList)
DirectProductFunctorialWithGivenDirectProducts
(CAP: DirectProductFunctorialWithGivenDirectProducts for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
DirectProductOnMorphisms
(CartesianCategories: DirectProductOnMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
DirectProductOnMorphismsWithGivenDirectProducts
(CartesianCategories: DirectProductOnMorphismsWithGivenDirectProducts for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
DirectSum
(CAP: DirectSum)
DirectSumFunctorial
(CAP: DirectSumFunctorial for IsList, IsList, IsList)
DirectSumFunctorialWithGivenDirectSums
(CAP: DirectSumFunctorialWithGivenDirectSums for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
DirectSumMorphismToWeakBiPushout
(FreydCategoriesForCAP: DirectSumMorphismToWeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism)
DistinguishedObjectOfHomomorphismStructure
(CAP: DistinguishedObjectOfHomomorphismStructure for IsCapCategory)
DualOnMorphisms
(MonoidalCategories: DualOnMorphisms for IsCapCategoryMorphism)
DualOnMorphismsWithGivenDuals
(MonoidalCategories: DualOnMorphismsWithGivenDuals for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
DualOnObjects
(MonoidalCategories: DualOnObjects for IsCapCategoryObject)
EmbeddingOfEqualizer
(CAP: EmbeddingOfEqualizer for IsCapCategoryObject, IsList)
EmbeddingOfEqualizerWithGivenEqualizer
(CAP: EmbeddingOfEqualizerWithGivenEqualizer for IsCapCategoryObject, IsList, IsCapCategoryObject)
EpimorphismFromSomeProjectiveObject
(CAP: EpimorphismFromSomeProjectiveObject for IsCapCategoryObject)
EpimorphismFromSomeProjectiveObjectForKernelObject
(FreydCategoriesForCAP: EpimorphismFromSomeProjectiveObjectForKernelObject for IsCapCategoryMorphism)
EpimorphismFromSomeProjectiveObjectForKernelObjectWithGivenSomeProjectiveObjectForKernelObject
(FreydCategoriesForCAP: EpimorphismFromSomeProjectiveObjectForKernelObjectWithGivenSomeProjectiveObjectForKernelObject for IsCapCategoryMorphism, IsCapCategoryObject)
EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject
(CAP: EpimorphismFromSomeProjectiveObjectWithGivenSomeProjectiveObject for IsCapCategoryObject, IsCapCategoryObject)
Equalizer
(CAP: Equalizer)
EqualizerFunctorial
(CAP: EqualizerFunctorial for IsList, IsCapCategoryMorphism, IsList)
EqualizerFunctorialWithGivenEqualizers
(CAP: EqualizerFunctorialWithGivenEqualizers for IsCapCategoryObject, IsList, IsCapCategoryMorphism, IsList, IsCapCategoryObject)
EvaluationForDual
(MonoidalCategories: EvaluationForDual for IsCapCategoryObject)
EvaluationForDualWithGivenTensorProduct
(MonoidalCategories: EvaluationForDualWithGivenTensorProduct for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
FiberProduct
(CAP: FiberProduct)
FiberProductFunctorial
(CAP: FiberProductFunctorial for IsList, IsList, IsList)
FiberProductFunctorialWithGivenFiberProducts
(CAP: FiberProductFunctorialWithGivenFiberProducts for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
HomologyObject
(CAP: HomologyObject for IsCapCategoryMorphism, IsCapCategoryMorphism)
HomologyObjectFunctorialWithGivenHomologyObjects
(CAP: HomologyObjectFunctorialWithGivenHomologyObjects for IsCapCategoryObject, IsList, IsCapCategoryObject)
HomomorphismStructureOnMorphisms
(CAP: HomomorphismStructureOnMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
HomomorphismStructureOnMorphismsWithGivenObjects
(CAP: HomomorphismStructureOnMorphismsWithGivenObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
HomomorphismStructureOnObjects
(CAP: HomomorphismStructureOnObjects for IsCapCategoryObject, IsCapCategoryObject)
IdentityMorphism
(CAP: IdentityMorphism for IsCapCategoryObject)
ImageEmbedding
(CAP: ImageEmbedding for IsCapCategoryMorphism)
ImageEmbeddingWithGivenImageObject
(CAP: ImageEmbeddingWithGivenImageObject for IsCapCategoryMorphism, IsCapCategoryObject)
ImageObject
(CAP: ImageObject for IsCapCategoryMorphism)
ImageObjectFunctorial
(CAP: ImageObjectFunctorial for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism)
ImageObjectFunctorialWithGivenImageObjects
(CAP: ImageObjectFunctorialWithGivenImageObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
InitialObject
(CAP: InitialObject for IsCapCategory)
InitialObjectFunctorial
(CAP: InitialObjectFunctorial for IsCapCategory)
InitialObjectFunctorialWithGivenInitialObjects
(CAP: InitialObjectFunctorialWithGivenInitialObjects for IsCapCategoryObject, IsCapCategoryObject)
InjectionOfBiasedWeakPushout
(FreydCategoriesForCAP: InjectionOfBiasedWeakPushout for IsCapCategoryMorphism, IsCapCategoryMorphism)
InjectionOfBiasedWeakPushoutWithGivenBiasedWeakPushout
(FreydCategoriesForCAP: InjectionOfBiasedWeakPushoutWithGivenBiasedWeakPushout for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
InjectionOfCofactorOfColimit
(ToolsForCategoricalTowers: InjectionOfCofactorOfColimit for IsList, IsList, IsInt)
InjectionOfCofactorOfColimitWithGivenColimit
(ToolsForCategoricalTowers: InjectionOfCofactorOfColimitWithGivenColimit for IsList, IsList, IsInt, IsCapCategoryObject)
InjectionOfCofactorOfCoproduct
(CAP: InjectionOfCofactorOfCoproduct for IsList, IsInt)
InjectionOfCofactorOfCoproductWithGivenCoproduct
(CAP: InjectionOfCofactorOfCoproductWithGivenCoproduct for IsList, IsInt, IsCapCategoryObject)
InjectionOfCofactorOfDirectSum
(CAP: InjectionOfCofactorOfDirectSum for IsList, IsInt)
InjectionOfCofactorOfDirectSumWithGivenDirectSum
(CAP: InjectionOfCofactorOfDirectSumWithGivenDirectSum for IsList, IsInt, IsCapCategoryObject)
InjectionOfCofactorOfPushout
(CAP: InjectionOfCofactorOfPushout for IsList, IsInt)
InjectionOfCofactorOfPushoutWithGivenPushout
(CAP: InjectionOfCofactorOfPushoutWithGivenPushout for IsList, IsInt, IsCapCategoryObject)
InjectionOfFirstCofactorOfWeakBiPushout
(FreydCategoriesForCAP: InjectionOfFirstCofactorOfWeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism)
InjectionOfFirstCofactorOfWeakBiPushoutWithGivenWeakBiPushout
(FreydCategoriesForCAP: InjectionOfFirstCofactorOfWeakBiPushoutWithGivenWeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
InjectionOfSecondCofactorOfWeakBiPushout
(FreydCategoriesForCAP: InjectionOfSecondCofactorOfWeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism)
InjectionOfSecondCofactorOfWeakBiPushoutWithGivenWeakBiPushout
(FreydCategoriesForCAP: InjectionOfSecondCofactorOfWeakBiPushoutWithGivenWeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
InjectiveColift
(CAP: InjectiveColift for IsCapCategoryMorphism, IsCapCategoryMorphism)
InternalHomOnMorphisms
(MonoidalCategories: InternalHomOnMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
InternalHomOnMorphismsWithGivenInternalHoms
(MonoidalCategories: InternalHomOnMorphismsWithGivenInternalHoms for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
InternalHomOnObjects
(MonoidalCategories: InternalHomOnObjects for IsCapCategoryObject, IsCapCategoryObject)
InternalHomToTensorProductLeftAdjunctMorphism
(MonoidalCategories: InternalHomToTensorProductLeftAdjunctMorphism for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism)
InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct
(MonoidalCategories: InternalHomToTensorProductLeftAdjunctMorphismWithGivenTensorProduct for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
InternalHomToTensorProductRightAdjunctMorphism
(MonoidalCategories: InternalHomToTensorProductRightAdjunctMorphism for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism)
InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct
(MonoidalCategories: InternalHomToTensorProductRightAdjunctMorphismWithGivenTensorProduct for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure
(CAP: InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructure for IsCapCategoryMorphism)
InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects
(CAP: InterpretMorphismAsMorphismFromDistinguishedObjectToHomomorphismStructureWithGivenObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism
(CAP: InterpretMorphismFromDistinguishedObjectToHomomorphismStructureAsMorphism for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism)
InverseForMorphisms
(CAP: InverseForMorphisms for IsCapCategoryMorphism)
InverseOfMorphismFromCoimageToImage
(CAP: InverseOfMorphismFromCoimageToImage for IsCapCategoryMorphism)
InverseOfMorphismFromCoimageToImageWithGivenObjects
(CAP: InverseOfMorphismFromCoimageToImageWithGivenObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
IsAutomorphism
(CAP: IsAutomorphism for IsCapCategoryMorphism)
IsCodominating
(CAP: IsCodominating for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsCongruentForMorphisms
(CAP: IsCongruentForMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsDominating
(CAP: IsDominating for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsEndomorphism
(CAP: IsEndomorphism for IsCapCategoryMorphism)
IsEpimorphism
(CAP: IsEpimorphism for IsCapCategoryMorphism)
IsEqualAsFactorobjects
(CAP: IsEqualAsFactorobjects for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsEqualAsSubobjects
(CAP: IsEqualAsSubobjects for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsEqualForMorphisms
(CAP: IsEqualForMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsEqualForMorphismsOnMor
(CAP: IsEqualForMorphismsOnMor for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsEqualForObjects
(CAP: IsEqualForObjects for IsCapCategoryObject, IsCapCategoryObject)
IsEqualToIdentityMorphism
(CAP: IsEqualToIdentityMorphism for IsCapCategoryMorphism)
IsEqualToZeroMorphism
(CAP: IsEqualToZeroMorphism for IsCapCategoryMorphism)
IsIdempotent
(CAP: IsIdempotent for IsCapCategoryMorphism)
IsInitial
(CAP: IsInitial for IsCapCategoryObject)
IsIsomorphism
(CAP: IsIsomorphism for IsCapCategoryMorphism)
IsMonomorphism
(CAP: IsMonomorphism for IsCapCategoryMorphism)
IsTerminal
(CAP: IsTerminal for IsCapCategoryObject)
IsWellDefinedForMorphisms
(CAP: IsWellDefinedForMorphisms for IsCapCategoryMorphism)
IsWellDefinedForMorphismsWithGivenSourceAndRange
(CAP: IsWellDefinedForMorphismsWithGivenSourceAndRange for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
IsWellDefinedForObjects
(CAP: IsWellDefinedForObjects for IsCapCategoryObject)
IsZeroForMorphisms
(CAP: IsZeroForMorphisms for IsCapCategoryMorphism)
IsZeroForObjects
(CAP: IsZeroForObjects for IsCapCategoryObject)
IsomorphismFromCoequalizerOfCoproductDiagramToPushout
(CAP: IsomorphismFromCoequalizerOfCoproductDiagramToPushout for IsList)
IsomorphismFromCoequalizerToCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproduct
(CAP: IsomorphismFromCoequalizerToCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproduct for IsCapCategoryObject, IsList)
IsomorphismFromCoimageToCokernelOfKernel
(CAP: IsomorphismFromCoimageToCokernelOfKernel for IsCapCategoryMorphism)
IsomorphismFromCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproductToCoequalizer
(CAP: IsomorphismFromCokernelOfJointPairwiseDifferencesOfMorphismsFromCoproductToCoequalizer for IsCapCategoryObject, IsList)
IsomorphismFromCokernelOfKernelToCoimage
(CAP: IsomorphismFromCokernelOfKernelToCoimage for IsCapCategoryMorphism)
IsomorphismFromCoproductToDirectSum
(CAP: IsomorphismFromCoproductToDirectSum for IsList)
IsomorphismFromDirectProductToDirectSum
(CAP: IsomorphismFromDirectProductToDirectSum for IsList)
IsomorphismFromDirectSumToCoproduct
(CAP: IsomorphismFromDirectSumToCoproduct for IsList)
IsomorphismFromDirectSumToDirectProduct
(CAP: IsomorphismFromDirectSumToDirectProduct for IsList)
IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct
(CAP: IsomorphismFromEqualizerOfDirectProductDiagramToFiberProduct for IsList)
IsomorphismFromEqualizerToKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProduct
(CAP: IsomorphismFromEqualizerToKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProduct for IsCapCategoryObject, IsList)
IsomorphismFromFiberProductToEqualizerOfDirectProductDiagram
(CAP: IsomorphismFromFiberProductToEqualizerOfDirectProductDiagram for IsList)
IsomorphismFromHomologyObjectToItsConstructionAsAnImageObject
(CAP: IsomorphismFromHomologyObjectToItsConstructionAsAnImageObject for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsomorphismFromImageObjectToKernelOfCokernel
(CAP: IsomorphismFromImageObjectToKernelOfCokernel for IsCapCategoryMorphism)
IsomorphismFromInitialObjectToZeroObject
(CAP: IsomorphismFromInitialObjectToZeroObject for IsCapCategory)
IsomorphismFromInternalHomToObject
(MonoidalCategories: IsomorphismFromInternalHomToObject for IsCapCategoryObject)
IsomorphismFromInternalHomToObjectWithGivenInternalHom
(MonoidalCategories: IsomorphismFromInternalHomToObjectWithGivenInternalHom for IsCapCategoryObject, IsCapCategoryObject)
IsomorphismFromItsConstructionAsAnImageObjectToHomologyObject
(CAP: IsomorphismFromItsConstructionAsAnImageObjectToHomologyObject for IsCapCategoryMorphism, IsCapCategoryMorphism)
IsomorphismFromKernelOfCokernelToImageObject
(CAP: IsomorphismFromKernelOfCokernelToImageObject for IsCapCategoryMorphism)
IsomorphismFromKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProductToEqualizer
(CAP: IsomorphismFromKernelOfJointPairwiseDifferencesOfMorphismsIntoDirectProductToEqualizer for IsCapCategoryObject, IsList)
IsomorphismFromObjectToInternalHom
(MonoidalCategories: IsomorphismFromObjectToInternalHom for IsCapCategoryObject)
IsomorphismFromObjectToInternalHomWithGivenInternalHom
(MonoidalCategories: IsomorphismFromObjectToInternalHomWithGivenInternalHom for IsCapCategoryObject, IsCapCategoryObject)
IsomorphismFromPushoutToCoequalizerOfCoproductDiagram
(CAP: IsomorphismFromPushoutToCoequalizerOfCoproductDiagram for IsList)
IsomorphismFromTerminalObjectToZeroObject
(CAP: IsomorphismFromTerminalObjectToZeroObject for IsCapCategory)
IsomorphismFromZeroObjectToInitialObject
(CAP: IsomorphismFromZeroObjectToInitialObject for IsCapCategory)
IsomorphismFromZeroObjectToTerminalObject
(CAP: IsomorphismFromZeroObjectToTerminalObject for IsCapCategory)
JointPairwiseDifferencesOfMorphismsFromCoproduct
(CAP: JointPairwiseDifferencesOfMorphismsFromCoproduct for IsCapCategoryObject, IsList)
JointPairwiseDifferencesOfMorphismsIntoDirectProduct
(CAP: JointPairwiseDifferencesOfMorphismsIntoDirectProduct for IsCapCategoryObject, IsList)
KernelEmbedding
(CAP: KernelEmbedding for IsCapCategoryMorphism)
KernelEmbeddingWithGivenKernelObject
(CAP: KernelEmbeddingWithGivenKernelObject for IsCapCategoryMorphism, IsCapCategoryObject)
KernelLift
(CAP: KernelLift for IsCapCategoryMorphism, IsCapCategoryObject, IsCapCategoryMorphism)
KernelLiftWithGivenKernelObject
(CAP: KernelLiftWithGivenKernelObject for IsCapCategoryMorphism, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
KernelObject
(CAP: KernelObject for IsCapCategoryMorphism)
KernelObjectFunctorial
(CAP: KernelObjectFunctorial for IsList)
KernelObjectFunctorialWithGivenKernelObjects
(CAP: KernelObjectFunctorialWithGivenKernelObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism,IsCapCategoryMorphism, IsCapCategoryObject)
LambdaElimination
(MonoidalCategories: LambdaElimination for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism)
LambdaIntroduction
(MonoidalCategories: LambdaIntroduction for IsCapCategoryMorphism)
LeftCartesianDistributivityFactoring
(CartesianCategories: LeftCartesianDistributivityFactoring for IsCapCategoryObject, IsList)
LeftCartesianDistributivityFactoringWithGivenObjects
(CartesianCategories: LeftCartesianDistributivityFactoringWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsList, IsCapCategoryObject)
LeftCocartesianCodistributivityExpanding
(CartesianCategories: LeftCocartesianCodistributivityExpanding for IsCapCategoryObject, IsList)
LeftCocartesianCodistributivityExpandingWithGivenObjects
(CartesianCategories: LeftCocartesianCodistributivityExpandingWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsList, IsCapCategoryObject)
LeftDistributivityExpanding
(MonoidalCategories: LeftDistributivityExpanding for IsCapCategoryObject, IsList)
LeftDistributivityExpandingWithGivenObjects
(MonoidalCategories: LeftDistributivityExpandingWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsList, IsCapCategoryObject)
LeftDistributivityFactoring
(MonoidalCategories: LeftDistributivityFactoring for IsCapCategoryObject, IsList)
LeftDistributivityFactoringWithGivenObjects
(MonoidalCategories: LeftDistributivityFactoringWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsList, IsCapCategoryObject)
LeftUnitor
(MonoidalCategories: LeftUnitor for IsCapCategoryObject)
LeftUnitorInverse
(MonoidalCategories: LeftUnitorInverse for IsCapCategoryObject)
LeftUnitorInverseWithGivenTensorProduct
(MonoidalCategories: LeftUnitorInverseWithGivenTensorProduct for IsCapCategoryObject, IsCapCategoryObject)
LeftUnitorWithGivenTensorProduct
(MonoidalCategories: LeftUnitorWithGivenTensorProduct for IsCapCategoryObject, IsCapCategoryObject)
Lift
(CAP: Lift for IsCapCategoryMorphism, IsCapCategoryMorphism)
LiftAlongMonomorphism
(CAP: LiftAlongMonomorphism for IsCapCategoryMorphism, IsCapCategoryMorphism)
MereExistenceOfUniqueSolutionOfHomogeneousLinearSystemInAbCategory
(ToolsForCategoricalTowers: MereExistenceOfUniqueSolutionOfHomogeneousLinearSystemInAbCategory for IsList, IsList)
MonoidalPostComposeMorphism
(MonoidalCategories: MonoidalPostComposeMorphism for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
MonoidalPostComposeMorphismWithGivenObjects
(MonoidalCategories: MonoidalPostComposeMorphismWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
MonoidalPreComposeMorphism
(MonoidalCategories: MonoidalPreComposeMorphism for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
MonoidalPreComposeMorphismWithGivenObjects
(MonoidalCategories: MonoidalPreComposeMorphismWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
MorphismBetweenCoproducts
(ToolsForCategoricalTowers: MorphismBetweenCoproducts for IsList, IsList, IsList)
MorphismBetweenCoproductsWithGivenCoproducts
(ToolsForCategoricalTowers: MorphismBetweenCoproductsWithGivenCoproducts for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
MorphismBetweenDirectProducts
(ToolsForCategoricalTowers: MorphismBetweenDirectProducts for IsList, IsList, IsList)
MorphismBetweenDirectProductsWithGivenDirectProducts
(ToolsForCategoricalTowers: MorphismBetweenDirectProductsWithGivenDirectProducts for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
MorphismBetweenDirectSums
(CAP: MorphismBetweenDirectSums for IsList, IsList, IsList)
MorphismBetweenDirectSumsWithGivenDirectSums
(CAP: MorphismBetweenDirectSumsWithGivenDirectSums for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
MorphismFromCoimageToImage
(CAP: MorphismFromCoimageToImage for IsCapCategoryMorphism)
MorphismFromCoimageToImageWithGivenObjects
(CAP: MorphismFromCoimageToImageWithGivenObjects for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
MorphismFromEqualizerToSink
(CAP: MorphismFromEqualizerToSink for IsCapCategoryObject, IsList)
MorphismFromEqualizerToSinkWithGivenEqualizer
(CAP: MorphismFromEqualizerToSinkWithGivenEqualizer for IsCapCategoryObject, IsList, IsCapCategoryObject)
MorphismFromFiberProductToSink
(CAP: MorphismFromFiberProductToSink for IsList)
MorphismFromFiberProductToSinkWithGivenFiberProduct
(CAP: MorphismFromFiberProductToSinkWithGivenFiberProduct for IsList, IsCapCategoryObject)
MorphismFromKernelObjectToSink
(CAP: MorphismFromKernelObjectToSink for IsCapCategoryMorphism)
MorphismFromKernelObjectToSinkWithGivenKernelObject
(CAP: MorphismFromKernelObjectToSinkWithGivenKernelObject for IsCapCategoryMorphism, IsCapCategoryObject)
MorphismFromSourceToCoequalizer
(CAP: MorphismFromSourceToCoequalizer for IsCapCategoryObject, IsList)
MorphismFromSourceToCoequalizerWithGivenCoequalizer
(CAP: MorphismFromSourceToCoequalizerWithGivenCoequalizer for IsCapCategoryObject, IsList, IsCapCategoryObject)
MorphismFromSourceToCokernelObject
(CAP: MorphismFromSourceToCokernelObject for IsCapCategoryMorphism)
MorphismFromSourceToCokernelObjectWithGivenCokernelObject
(CAP: MorphismFromSourceToCokernelObjectWithGivenCokernelObject for IsCapCategoryMorphism, IsCapCategoryObject)
MorphismFromSourceToPushout
(CAP: MorphismFromSourceToPushout for IsList)
MorphismFromSourceToPushoutWithGivenPushout
(CAP: MorphismFromSourceToPushoutWithGivenPushout for IsList, IsCapCategoryObject)
MorphismFromTensorProductToInternalHom
(MonoidalCategories: MorphismFromTensorProductToInternalHom for IsCapCategoryObject, IsCapCategoryObject)
MorphismFromTensorProductToInternalHomWithGivenObjects
(MonoidalCategories: MorphismFromTensorProductToInternalHomWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
MorphismToBidual
(MonoidalCategories: MorphismToBidual for IsCapCategoryObject)
MorphismToBidualWithGivenBidual
(MonoidalCategories: MorphismToBidualWithGivenBidual for IsCapCategoryObject, IsCapCategoryObject)
PostCompose
(CAP: PostCompose for IsCapCategoryMorphism, IsCapCategoryMorphism)
PostComposeList
(CAP: PostComposeList for IsCapCategoryObject, IsList, IsCapCategoryObject)
PostInverseForMorphisms
(CAP: PostInverseForMorphisms for IsCapCategoryMorphism)
PreCompose
(CAP: PreCompose for IsCapCategoryMorphism, IsCapCategoryMorphism)
PreComposeList
(CAP: PreComposeList for IsCapCategoryObject, IsList, IsCapCategoryObject)
PreInverseForMorphisms
(CAP: PreInverseForMorphisms for IsCapCategoryMorphism)
ProjectionInFactorOfDirectProduct
(CAP: ProjectionInFactorOfDirectProduct for IsList, IsInt)
ProjectionInFactorOfDirectProductWithGivenDirectProduct
(CAP: ProjectionInFactorOfDirectProductWithGivenDirectProduct for IsList, IsInt, IsCapCategoryObject)
ProjectionInFactorOfDirectSum
(CAP: ProjectionInFactorOfDirectSum for IsList, IsInt)
ProjectionInFactorOfDirectSumWithGivenDirectSum
(CAP: ProjectionInFactorOfDirectSumWithGivenDirectSum for IsList, IsInt, IsCapCategoryObject)
ProjectionInFactorOfFiberProduct
(CAP: ProjectionInFactorOfFiberProduct for IsList, IsInt)
ProjectionInFactorOfFiberProductWithGivenFiberProduct
(CAP: ProjectionInFactorOfFiberProductWithGivenFiberProduct for IsList, IsInt, IsCapCategoryObject)
ProjectionInFactorOfLimit
(ToolsForCategoricalTowers: ProjectionInFactorOfLimit for IsList, IsList, IsInt)
ProjectionInFactorOfLimitWithGivenLimit
(ToolsForCategoricalTowers: ProjectionInFactorOfLimitWithGivenLimit for IsList, IsList, IsInt, IsCapCategoryObject)
ProjectionInFirstFactorOfWeakBiFiberProduct
(FreydCategoriesForCAP: ProjectionInFirstFactorOfWeakBiFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism)
ProjectionInFirstFactorOfWeakBiFiberProductWithGivenWeakBiFiberProduct
(FreydCategoriesForCAP: ProjectionInFirstFactorOfWeakBiFiberProductWithGivenWeakBiFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
ProjectionInSecondFactorOfWeakBiFiberProduct
(FreydCategoriesForCAP: ProjectionInSecondFactorOfWeakBiFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism)
ProjectionInSecondFactorOfWeakBiFiberProductWithGivenWeakBiFiberProduct
(FreydCategoriesForCAP: ProjectionInSecondFactorOfWeakBiFiberProductWithGivenWeakBiFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
ProjectionOfBiasedWeakFiberProduct
(FreydCategoriesForCAP: ProjectionOfBiasedWeakFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism)
ProjectionOfBiasedWeakFiberProductWithGivenBiasedWeakFiberProduct
(FreydCategoriesForCAP: ProjectionOfBiasedWeakFiberProductWithGivenBiasedWeakFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
ProjectionOntoCoequalizer
(CAP: ProjectionOntoCoequalizer for IsCapCategoryObject, IsList)
ProjectionOntoCoequalizerWithGivenCoequalizer
(CAP: ProjectionOntoCoequalizerWithGivenCoequalizer for IsCapCategoryObject, IsList, IsCapCategoryObject)
ProjectiveLift
(CAP: ProjectiveLift for IsCapCategoryMorphism, IsCapCategoryMorphism)
Pushout
(CAP: Pushout for IsList)
PushoutFunctorial
(CAP: PushoutFunctorial for IsList, IsList, IsList)
PushoutFunctorialWithGivenPushouts
(CAP: PushoutFunctorialWithGivenPushouts for IsCapCategoryObject, IsList, IsList, IsList, IsCapCategoryObject)
RightCartesianDistributivityFactoring
(CartesianCategories: RightCartesianDistributivityFactoring for IsList, IsCapCategoryObject)
RightCartesianDistributivityFactoringWithGivenObjects
(CartesianCategories: RightCartesianDistributivityFactoringWithGivenObjects for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryObject)
RightCocartesianCodistributivityExpanding
(CartesianCategories: RightCocartesianCodistributivityExpanding for IsList, IsCapCategoryObject)
RightCocartesianCodistributivityExpandingWithGivenObjects
(CartesianCategories: RightCocartesianCodistributivityExpandingWithGivenObjects for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryObject)
RightDistributivityExpanding
(MonoidalCategories: RightDistributivityExpanding for IsList, IsCapCategoryObject)
RightDistributivityExpandingWithGivenObjects
(MonoidalCategories: RightDistributivityExpandingWithGivenObjects for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryObject)
RightDistributivityFactoring
(MonoidalCategories: RightDistributivityFactoring for IsList, IsCapCategoryObject)
RightDistributivityFactoringWithGivenObjects
(MonoidalCategories: RightDistributivityFactoringWithGivenObjects for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryObject)
RightUnitor
(MonoidalCategories: RightUnitor for IsCapCategoryObject)
RightUnitorInverse
(MonoidalCategories: RightUnitorInverse for IsCapCategoryObject)
RightUnitorInverseWithGivenTensorProduct
(MonoidalCategories: RightUnitorInverseWithGivenTensorProduct for IsCapCategoryObject, IsCapCategoryObject)
RightUnitorWithGivenTensorProduct
(MonoidalCategories: RightUnitorWithGivenTensorProduct for IsCapCategoryObject, IsCapCategoryObject)
SolveLinearSystemInAbCategory
(CAP: SolveLinearSystemInAbCategory for IsList, IsList, IsList)
SomeProjectiveObject
(CAP: SomeProjectiveObject for IsCapCategoryObject)
SomeProjectiveObjectForKernelObject
(FreydCategoriesForCAP: SomeProjectiveObjectForKernelObject for IsCapCategoryMorphism)
SubtractionForMorphisms
(CAP: SubtractionForMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
SumOfMorphisms
(CAP: SumOfMorphisms for IsCapCategoryObject, IsList, IsCapCategoryObject)
TensorProductDualityCompatibilityMorphism
(MonoidalCategories: TensorProductDualityCompatibilityMorphism for IsCapCategoryObject, IsCapCategoryObject)
TensorProductDualityCompatibilityMorphismWithGivenObjects
(MonoidalCategories: TensorProductDualityCompatibilityMorphismWithGivenObjects for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryObject)
TensorProductInternalHomCompatibilityMorphism
(MonoidalCategories: TensorProductInternalHomCompatibilityMorphism for IsList)
TensorProductInternalHomCompatibilityMorphismWithGivenObjects
(MonoidalCategories: TensorProductInternalHomCompatibilityMorphismWithGivenObjects for IsCapCategoryObject, IsList, IsCapCategoryObject)
TensorProductOnMorphisms
(MonoidalCategories: TensorProductOnMorphisms for IsCapCategoryMorphism, IsCapCategoryMorphism)
TensorProductOnMorphismsWithGivenTensorProducts
(MonoidalCategories: TensorProductOnMorphismsWithGivenTensorProducts for IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
TensorProductOnObjects
(MonoidalCategories: TensorProductOnObjects for IsCapCategoryObject, IsCapCategoryObject)
TensorProductToInternalHomLeftAdjunctMorphism
(MonoidalCategories: TensorProductToInternalHomLeftAdjunctMorphism for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism)
TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom
(MonoidalCategories: TensorProductToInternalHomLeftAdjunctMorphismWithGivenInternalHom for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
TensorProductToInternalHomRightAdjunctMorphism
(MonoidalCategories: TensorProductToInternalHomRightAdjunctMorphism for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism)
TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom
(MonoidalCategories: TensorProductToInternalHomRightAdjunctMorphismWithGivenInternalHom for IsCapCategoryObject, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
TensorUnit
(MonoidalCategories: TensorUnit for IsCapCategory)
TerminalObject
(CAP: TerminalObject for IsCapCategory)
TerminalObjectFunctorial
(CAP: TerminalObjectFunctorial for IsCapCategory)
TerminalObjectFunctorialWithGivenTerminalObjects
(CAP: TerminalObjectFunctorialWithGivenTerminalObjects for IsCapCategoryObject, IsCapCategoryObject)
UniversalMorphismFromBiasedWeakPushout
(FreydCategoriesForCAP: UniversalMorphismFromBiasedWeakPushout for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism)
UniversalMorphismFromBiasedWeakPushoutWithGivenBiasedWeakPushout
(FreydCategoriesForCAP: UniversalMorphismFromBiasedWeakPushoutWithGivenBiasedWeakPushout for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
UniversalMorphismFromCoequalizer
(CAP: UniversalMorphismFromCoequalizer for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryMorphism)
UniversalMorphismFromCoequalizerWithGivenCoequalizer
(CAP: UniversalMorphismFromCoequalizerWithGivenCoequalizer for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
UniversalMorphismFromColimit
(ToolsForCategoricalTowers: UniversalMorphismFromColimit for IsList, IsList, IsCapCategoryObject, IsList)
UniversalMorphismFromColimitWithGivenColimit
(ToolsForCategoricalTowers: UniversalMorphismFromColimitWithGivenColimit for IsList, IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismFromCoproduct
(CAP: UniversalMorphismFromCoproduct for IsList, IsCapCategoryObject, IsList)
UniversalMorphismFromCoproductWithGivenCoproduct
(CAP: UniversalMorphismFromCoproductWithGivenCoproduct for IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismFromDirectSum
(CAP: UniversalMorphismFromDirectSum for IsList, IsCapCategoryObject, IsList)
UniversalMorphismFromDirectSumWithGivenDirectSum
(CAP: UniversalMorphismFromDirectSumWithGivenDirectSum for IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismFromImage
(CAP: UniversalMorphismFromImage for IsCapCategoryMorphism, IsList)
UniversalMorphismFromImageWithGivenImageObject
(CAP: UniversalMorphismFromImageWithGivenImageObject for IsCapCategoryMorphism, IsList, IsCapCategoryObject)
UniversalMorphismFromInitialObject
(CAP: UniversalMorphismFromInitialObject for IsCapCategoryObject)
UniversalMorphismFromInitialObjectWithGivenInitialObject
(CAP: UniversalMorphismFromInitialObjectWithGivenInitialObject for IsCapCategoryObject, IsCapCategoryObject)
UniversalMorphismFromPushout
(CAP: UniversalMorphismFromPushout for IsList, IsCapCategoryObject, IsList)
UniversalMorphismFromPushoutWithGivenPushout
(CAP: UniversalMorphismFromPushoutWithGivenPushout for IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismFromWeakBiPushout
(FreydCategoriesForCAP: UniversalMorphismFromWeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism)
UniversalMorphismFromWeakBiPushoutWithGivenWeakBiPushout
(FreydCategoriesForCAP: UniversalMorphismFromWeakBiPushoutWithGivenWeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
UniversalMorphismFromZeroObject
(CAP: UniversalMorphismFromZeroObject for IsCapCategoryObject)
UniversalMorphismFromZeroObjectWithGivenZeroObject
(CAP: UniversalMorphismFromZeroObjectWithGivenZeroObject for IsCapCategoryObject, IsCapCategoryObject)
UniversalMorphismIntoBiasedWeakFiberProduct
(FreydCategoriesForCAP: UniversalMorphismIntoBiasedWeakFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism)
UniversalMorphismIntoBiasedWeakFiberProductWithGivenBiasedWeakFiberProduct
(FreydCategoriesForCAP: UniversalMorphismIntoBiasedWeakFiberProductWithGivenBiasedWeakFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
UniversalMorphismIntoCoimage
(CAP: UniversalMorphismIntoCoimage for IsCapCategoryMorphism, IsList)
UniversalMorphismIntoCoimageWithGivenCoimageObject
(CAP: UniversalMorphismIntoCoimageWithGivenCoimageObject for IsCapCategoryMorphism, IsList, IsCapCategoryObject)
UniversalMorphismIntoDirectProduct
(CAP: UniversalMorphismIntoDirectProduct for IsList, IsCapCategoryObject, IsList)
UniversalMorphismIntoDirectProductWithGivenDirectProduct
(CAP: UniversalMorphismIntoDirectProductWithGivenDirectProduct for IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismIntoDirectSum
(CAP: UniversalMorphismIntoDirectSum for IsList, IsCapCategoryObject, IsList)
UniversalMorphismIntoDirectSumWithGivenDirectSum
(CAP: UniversalMorphismIntoDirectSumWithGivenDirectSum for IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismIntoEqualizer
(CAP: UniversalMorphismIntoEqualizer for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryMorphism)
UniversalMorphismIntoEqualizerWithGivenEqualizer
(CAP: UniversalMorphismIntoEqualizerWithGivenEqualizer for IsCapCategoryObject, IsList, IsCapCategoryObject, IsCapCategoryMorphism, IsCapCategoryObject)
UniversalMorphismIntoFiberProduct
(CAP: UniversalMorphismIntoFiberProduct for IsList, IsCapCategoryObject, IsList)
UniversalMorphismIntoFiberProductWithGivenFiberProduct
(CAP: UniversalMorphismIntoFiberProductWithGivenFiberProduct for IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismIntoLimit
(ToolsForCategoricalTowers: UniversalMorphismIntoLimit for IsList, IsList, IsCapCategoryObject, IsList)
UniversalMorphismIntoLimitWithGivenLimit
(ToolsForCategoricalTowers: UniversalMorphismIntoLimitWithGivenLimit for IsList, IsList, IsCapCategoryObject, IsList, IsCapCategoryObject)
UniversalMorphismIntoTerminalObject
(CAP: UniversalMorphismIntoTerminalObject for IsCapCategoryObject)
UniversalMorphismIntoTerminalObjectWithGivenTerminalObject
(CAP: UniversalMorphismIntoTerminalObjectWithGivenTerminalObject for IsCapCategoryObject, IsCapCategoryObject)
UniversalMorphismIntoWeakBiFiberProduct
(FreydCategoriesForCAP: UniversalMorphismIntoWeakBiFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism)
UniversalMorphismIntoWeakBiFiberProductWithGivenWeakBiFiberProduct
(FreydCategoriesForCAP: UniversalMorphismIntoWeakBiFiberProductWithGivenWeakBiFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
UniversalMorphismIntoZeroObject
(CAP: UniversalMorphismIntoZeroObject for IsCapCategoryObject)
UniversalMorphismIntoZeroObjectWithGivenZeroObject
(CAP: UniversalMorphismIntoZeroObjectWithGivenZeroObject for IsCapCategoryObject, IsCapCategoryObject)
WeakBiFiberProduct
(FreydCategoriesForCAP: WeakBiFiberProduct for IsCapCategoryMorphism, IsCapCategoryMorphism)
WeakBiFiberProductMorphismToDirectSum
(FreydCategoriesForCAP: WeakBiFiberProductMorphismToDirectSum for IsCapCategoryMorphism, IsCapCategoryMorphism)
WeakBiPushout
(FreydCategoriesForCAP: WeakBiPushout for IsCapCategoryMorphism, IsCapCategoryMorphism)
WeakCokernelColift
(FreydCategoriesForCAP: WeakCokernelColift for IsCapCategoryMorphism, IsCapCategoryMorphism)
WeakCokernelColiftWithGivenWeakCokernelObject
(FreydCategoriesForCAP: WeakCokernelColiftWithGivenWeakCokernelObject for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
WeakCokernelObject
(FreydCategoriesForCAP: WeakCokernelObject for IsCapCategoryMorphism)
WeakCokernelProjection
(FreydCategoriesForCAP: WeakCokernelProjection for IsCapCategoryMorphism)
WeakCokernelProjectionWithGivenWeakCokernelObject
(FreydCategoriesForCAP: WeakCokernelProjectionWithGivenWeakCokernelObject for IsCapCategoryMorphism, IsCapCategoryObject)
WeakKernelEmbedding
(FreydCategoriesForCAP: WeakKernelEmbedding for IsCapCategoryMorphism)
WeakKernelEmbeddingWithGivenWeakKernelObject
(FreydCategoriesForCAP: WeakKernelEmbeddingWithGivenWeakKernelObject for IsCapCategoryMorphism, IsCapCategoryObject)
WeakKernelLift
(FreydCategoriesForCAP: WeakKernelLift for IsCapCategoryMorphism, IsCapCategoryMorphism)
WeakKernelLiftWithGivenWeakKernelObject
(FreydCategoriesForCAP: WeakKernelLiftWithGivenWeakKernelObject for IsCapCategoryMorphism, IsCapCategoryMorphism, IsCapCategoryObject)
WeakKernelObject
(FreydCategoriesForCAP: WeakKernelObject for IsCapCategoryMorphism)
ZeroMorphism
(CAP: ZeroMorphism for IsCapCategoryObject, IsCapCategoryObject)
ZeroObject
(CAP: ZeroObject for IsCapCategory)
ZeroObjectFunctorial
(CAP: ZeroObjectFunctorial for IsCapCategory)
ZeroObjectFunctorialWithGivenZeroObjects
(CAP: ZeroObjectFunctorialWithGivenZeroObjects for IsCapCategoryObject, IsCapCategoryObject)
‣ IsCategoryOfHomalgGradedModules ( arg ) | ( filter ) |
Returns: true
or false
generated by GAPDoc2HTML