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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