Here we assume that the object set of the source category carries a discrete total order. This code is temporary and should at some point in the future be replaced by something like "presheaves with bounded support".
‣ IsPreSheafWithBoundsCategory( category ) | ( filter ) |
Returns: true or false
The GAP category of a presheaf category.
‣ IsCellInPreSheafWithBoundsCategory( cell ) | ( filter ) |
Returns: true or false
The GAP category of cells in a presheaf category.
‣ IsObjectInPreSheafWithBoundsCategory( obj ) | ( filter ) |
Returns: true or false
The GAP category of objects in a presheaf category.
‣ IsMorphismInPreSheafWithBoundsCategory( mor ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a presheaf category.
‣ Source( PSh ) | ( attribute ) |
Returns: a CAP category
The source category \(C\) of the presheaf category PSh=PSh(\(C,V\)).
‣ Target( PSh ) | ( attribute ) |
Returns: a CAP category
The target category \(V\) of the presheaf category PSh=PSh(\(C,V\)).
‣ OppositeOfSource( Hom ) | ( attribute ) |
Returns: a CAP category
The opposite \(C^\mathrm{op}\) of the source category \(C\) of the presheaf category PSh=PSh(\(C,V\)).
‣ Source( F ) | ( attribute ) |
Returns: a CAP category
The source of the presheaf F.
‣ Target( F ) | ( attribute ) |
Returns: a CAP category
The target of the presheaf F.
‣ YonedaEmbedding( B ) | ( attribute ) |
Returns: a CAP functor
‣ YonedaEmbeddingOfSourceCategory( PSh ) | ( attribute ) |
Returns: a CAP functor
‣ CoYonedaLemmaOnObjects( F ) | ( attribute ) |
‣ CoYonedaLemmaOnMorphisms( phi ) | ( attribute ) |
‣ PreSheavesWithBounds( B, C ) | ( operation ) |
‣ PreSheavesWithBounds( B ) | ( operation ) |
Returns: a CAP category
Construct the category Hom( B^op, C ) of functors from the opposite of the small category B to the category C as objects and their natural transformations as morphisms.
‣ ApplyObjectInPreSheafCategoryToObject( F, obj ) | ( operation ) |
Returns: a CAP object
Apply the presheaf F to the object obj. The shorthand is F(obj).
‣ ApplyObjectInPreSheafCategoryToMorphism( F, mor ) | ( operation ) |
Returns: a CAP morphism
Apply the presheaf F to the morphism mor. The shorthand is F(mor).
‣ ApplyMorphismInPreSheafCategoryToObject( eta, obj ) | ( operation ) |
Returns: a CAP morphism
Apply the presheaf morphism eta to the object obj. The shorthand is eta(o).
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