‣ FreeDistributiveCompletion( B ) | ( operation ) |
‣ FreeDistributiveCompletion( B, H ) | ( operation ) |
Returns: a CAP category
Construct a free distributive completion category.
‣ UnderlyingCategory( finite_completion ) | ( attribute ) |
‣ EmbeddingOfUnderlyingCategory( finite_completion ) | ( attribute ) |
Returns: a CAP functor
‣ IsFreeDistributiveCompletion( category ) | ( category ) |
Returns: true or false
The GAP category of a free distributive completion category.
‣ IsCellInFreeDistributiveCompletion( cell ) | ( category ) |
Returns: true or false
The GAP category of cells in a free distributive completion category.
‣ IsObjectInFreeDistributiveCompletion( obj ) | ( category ) |
Returns: true or false
The GAP category of objects in a free distributive completion category.
‣ IsMorphismInFreeDistributiveCompletion( mor ) | ( category ) |
Returns: true or false
The GAP category of morphisms in a free distributive completion category.
The category of presheaves with values in the interval category of the boolean algebra 2^2 has 6 distinct objects. This is the free distributive lattice generated by a discrete category with two objects.
gap> LoadPackage( "FunctorCategories", false ); true gap> pq := FinQuiver( "quiver(p,q)" ); FinQuiver( "quiver(p,q)[]" ) gap> F := PathCategory( pq ); PathCategory( FinQuiver( "quiver(p,q)[]" ) ) gap> P := PosetOfCategory( F ); PosetOfCategory( PathCategory( FinQuiver( "quiver(p,q)[]" ) ) ) gap> Dist := FreeDistributiveCompletion( P ); FreeDistributiveCompletion( PosetOfCategory( PathCategory( FinQuiver( "quiver(p,q)[]" ) ) ) ) gap> Display( Dist ); A CAP category with name FreeDistributiveCompletion( PosetOfCategory( PathCategory( FinQuiver( "quiver(p,q)[]" ) ) ) ): 25 primitive operations were used to derive 293 operations for this category which algorithmically * IsCategoryWithDecidableColifts * IsCategoryWithDecidableLifts * IsFiniteCategory * IsEquippedWithHomomorphismStructure * IsHeytingAlgebra and not yet algorithmically * IsBiHeytingAlgebra gap> Length( SetOfObjects( Dist ) ); 6 gap> Print( DotVertexLabelledDigraph( DigraphOfPoset( Dist : offset := 0 ) ) ); //dot digraph subobject_lattice{ rankdir="BT" minlen=0 node [shape=circle width=0 height=0 fontsize=12 margin=0.01 fontname="DejaVu Serif,serif"] edge [arrowsize=0.5] 1 [label="0"] 2 [label="1"] 3 [label="2"] 4 [label="3"] 5 [label="4"] 6 [label="5"] 1 -> 5 3 -> 6 4 -> 6 5 -> 3 5 -> 4 6 -> 2 } gap> DiffbCSL := MeetSemilatticeOfSingleDifferences( Dist ); MeetSemilatticeOfSingleDifferences( FreeDistributiveCompletion( PosetOfCategory( PathCategory( FinQuiver( "quiver(p,q)[]" ) ) ) ) ) gap> Length( SetOfObjects( DiffbCSL ) ); 13
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