‣ IsCapFullSubcategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of a full subcategory.
‣ IsCapFullSubcategoryGeneratedByFiniteNumberOfObjects( arg ) | ( filter ) |
Returns: true or false
The GAP category of a full subcategory generated by finite number of objects.
‣ IsCapFullSubcategoryDefinedByObjectMembershipFunction( arg ) | ( filter ) |
Returns: true or false
The GAP category of a full subcategory defined by an object-membership function.
‣ IsCellInAFullSubcategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of cells in a full subcategory.
‣ IsObjectInAFullSubcategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of objects in a full subcategory.
‣ IsMorphismInAFullSubcategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a full subcategory.
‣ CAP_INTERNAL_METHOD_NAME_LIST_FOR_FULL_SUBCATEGORY | ( global variable ) |
‣ CAP_INTERNAL_METHOD_NAME_LIST_FOR_ADDITIVE_FULL_SUBCATEGORY | ( global variable ) |
‣ FullSubcategory( C, name ) | ( operation ) |
‣ FullSubcategoryGeneratedByListOfObjects( L ) | ( function ) |
Returns: CapFullSubcategory
The input is a list of objects L in the same category. The output is the full subcategory generated by L.
‣ FullSubcategoryOfIndecomposableProjectiveObjects( C ) | ( attribute ) |
Returns: CapFullSubcategory
The input is a category C in which the operation IndecomposableProjectiveObjects is computable. The output is the full subcategory of C generated by the output of IndecomposableProjectiveObjects(C).
‣ FullSubcategoryOfIndecomposableInjectiveObjects( C ) | ( attribute ) |
Returns: CapFullSubcategory
The input is a category C in which the operation IndecomposableInjectiveObjects is computable. The output is the full subcategory of C generated by the output of IndecomposableInjectiveObjects(C).
‣ FullSubcategoryByObjectMembershipFunction( C, membership_func ) | ( function ) |
Returns: CapFullSubcategory
The input is a category C and an object membership function membership_func. The output is the full subcategory of C determined by membership_func.
‣ FullSubcategoryOfProjectiveObjects( C ) | ( attribute ) |
Returns: CapFullSubcategory
The input is an abelian category C with enough projective objects. The output is the full subcategory of C generated by the projective objects in C.
‣ FullSubcategoryOfInjectiveObjects( C ) | ( attribute ) |
Returns: CapFullSubcategory
The input is an abelian category C with enough injective objects. The output is the full subcategory of C generated by the injective objects in C.
‣ InclusionFunctor( A ) | ( attribute ) |
Returns: CapFunctor
The natural embedding functor from A to AmbientCategory(A).
‣ RestrictFunctorToFullSubcategoryOfSource( F, full ) | ( operation ) |
Returns: CapFunctor
The arguments are a functor F and a full subcategory full of Source(F). The output is the restriction functor \(F_{full}\):full\(\to\)Range(F).
‣ RestrictFunctorToFullSubcategoryOfRange( F, full ) | ( operation ) |
Returns: CapFunctor
The arguments are a functor F and a full subcategory full of Range(F). The output is the restriction functor \(F_{full}\):Source(F)\(\to\)full.
‣ RestrictFunctorToFullSubcategories( F, full_1, full_2 ) | ( operation ) |
Returns: CapFunctor
The arguments are a functor F and two full subcategories full_1 of Source(F) and full_2 of Range(F). The output is the restriction functor \(F_{full}\):full_1\(\to\)full_2.
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