‣ IsLazySliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of an eager slice category.
‣ IsCellInALazySliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of cells in an eager slice category.
‣ IsObjectInALazySliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of objects in an eager slice category.
‣ IsMorphismInALazySliceCategory( arg ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in an eager slice category.
‣ IsLazySliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of an eager slice category over the tensor unit.
‣ IsCellInALazySliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of cells in an eager slice category over the tensor unit.
‣ IsObjectInALazySliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of objects in an eager slice category over the tensor unit.
‣ IsMorphismInALazySliceCategoryOverTensorUnit( arg ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in an eager slice category over the tensor unit.
‣ UnderlyingMorphismList( object ) | ( attribute ) |
Returns: a list
The list of morphisms in the ambient category underlying object.
‣ LazySliceCategory( B ) | ( attribute ) |
‣ LazySliceCategoryOverTensorUnit( M ) | ( attribute ) |
‣ AsSliceCategoryCell( L ) | ( attribute ) |
gap> LoadPackage( "FinSetsForCAP", ">= 2022.05-05" ); true gap> B := FinSet( 2 ); |2| gap> o0 := AsSliceCategoryCell( [ MapOfFinSets( B, [ 1, 1 ], B ) ] ); An object in the lazy slice category given by: |2| → |2| gap> o1 := AsSliceCategoryCell( [ MapOfFinSets( FinSet( 3 ), [ 0, 1, 0 ], B ) ] ); An object in the lazy slice category given by: |3| → |2| gap> o2 := AsSliceCategoryCell( [ MapOfFinSets( FinSet( 4 ), [ 1, 0, 1, 0 ], B ) ] ); An object in the lazy slice category given by: |4| → |2| gap> IsWellDefined( o0 ); true gap> IsWellDefined( o1 ); true gap> IsWellDefined( o2 ); true gap> IsHomSetInhabited( o1, o0 ); false gap> IsHomSetInhabited( o0, o1 ); true gap> IsHomSetInhabited( o1, o2 ); true gap> IsHomSetInhabited( o2, o1 ); true gap> iota := UniversalMorphismFromInitialObject( o1 ); A morphism in the lazy slice category given by: |0| → |3| gap> Display( iota ); ∅ ⱶ[ ]→ { 0, 1, 2 } A morphism in the lazy slice category given by the above data gap> IsInitial( Source( iota ) ); true gap> tau := UniversalMorphismIntoTerminalObject( o2 ); A morphism in the lazy slice category given by: |4| → |2| gap> Display( tau ); { 0,..., 3 } ⱶ[ 1, 0, 1, 0 ]→ { 0, 1 } A morphism in the lazy slice category given by the above data gap> IsTerminal( Target( tau ) ); true gap> n := MapOfFinSets( FinSet( 3 ), [ 2, 0, 3 ], FinSet( 4 ) ); |3| → |4| gap> IsWellDefined( n ); true gap> n := AsSliceCategoryCell( o1, n, o2 ); A morphism in the lazy slice category given by: |3| → |4| gap> IsWellDefined( n ); false gap> m1 := MapOfFinSets( FinSet( 3 ), [ 1, 0, 3 ], FinSet( 4 ) ); |3| → |4| gap> m1 := AsSliceCategoryCell( o1, m1, o2 ); A morphism in the lazy slice category given by: |3| → |4| gap> IsWellDefined( m1 ); true gap> IsSplitEpimorphism( m1 ); false gap> m2 := MapOfFinSets( FinSet( 4 ), [ 1, 2, 1, 0 ], FinSet( 3 ) ); |4| → |3| gap> m2 := AsSliceCategoryCell( o2, m2, o1 ); A morphism in the lazy slice category given by: |4| → |3| gap> IsWellDefined( m2 ); true gap> IsSplitEpimorphism( m2 ); true gap> m3 := PreCompose( m1, m2 ); A morphism in the lazy slice category given by: |3| → |3| gap> IsWellDefined( m3 ); true gap> IsOne( m3 ); false gap> m4 := Inverse( m3 ); A morphism in the lazy slice category given by: |3| → |3| gap> IsWellDefined( m4 ); true gap> m5 := PreCompose( m2, m1 ); A morphism in the lazy slice category given by: |4| → |4| gap> IsWellDefined( m5 ); true gap> IsOne( m5 ); false
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