‣ IsSliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of a slice category.
‣ IsCellInASliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of cells in a slice category.
‣ IsObjectInASliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of objects in a slice category.
‣ IsMorphismInASliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a slice category.
‣ IsSliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of a slice category over the tensor unit.
‣ IsCellInSliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of cells in a slice category over the tensor unit.
‣ IsObjectInSliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of objects in a slice category over the tensor unit.
‣ IsMorphismInSliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a slice category over the tensor unit.
‣ CAP_INTERNAL_METHOD_NAME_LIST_FOR_SLICE_CATEGORY | ( global variable ) |
‣ AmbientCategory( S ) | ( attribute ) |
Returns: a list
The ambient category of the slice category S.
‣ BaseObject( S ) | ( attribute ) |
Returns: a CAP object
The base object of the slice category S.
‣ BaseObject( cell ) | ( attribute ) |
Returns: a CAP object
The base object underlying cell.
‣ UnderlyingMorphism( obj ) | ( attribute ) |
Returns: a CAP morphism
The morphism in the ambient category underlying the slice category object obj.
‣ SourceOfUnderlyingMorphism( obj ) | ( attribute ) |
Returns: a CAP object
The source of the morphism in the ambient category underlying the slice category object obj.
‣ UnderlyingCell( mor ) | ( attribute ) |
Returns: a CAP mor
The cell in the ambient category underlying the slice category morphism mor.
‣ InclusionFunctor( S ) | ( attribute ) |
Returns: a functor
The natural embedding functor from S to AmbientCategory(S).
‣ DualOverTensorUnit( J ) | ( attribute ) |
Returns: a CAP morphism
The argument is an object \(J \colon j \rightarrow 1\) in the slice category S over the tensor unit. The output is the dual morphism \(J^\vee \colon 1 \rightarrow \mathrm{\underline{Hom}}(j,1)\) in the ambient category of S.
‣ AsSliceCategoryCell( mor, S ) | ( operation ) |
‣ /( mor, S ) | ( operation ) |
‣ AsSliceCategoryCell( A, mor, B ) | ( operation ) |
‣ MorphismFromCovariantArgumentOfInternalHom( J, I ) | ( operation ) |
Returns: a morphism
The natural morphism \(I \to \mathrm{\underline{Hom}}(J,I)\), where I and J are objects in a slice category over the tensor unit.
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