‣ IsCapCategoryWithAmbientObjects( arg ) | ( filter ) |
Returns: true or false
The GAP category of lazy evaluated generalized embeddings in ambient objects.
‣ IsLazyGeneralizedEmbeddingInAmbientObject( arg ) | ( filter ) |
Returns: true or false
The GAP category of lazy evaluated generalized embeddings in ambient objects.
‣ IsCapCategoryObjectWithAmbientObject( arg ) | ( filter ) |
Returns: true or false
The GAP category of objects with ambient objects in a CAP category.
‣ IsCapCategoryMorphismWithAmbientObject( arg ) | ( filter ) |
Returns: true or false
The GAP category of morphisms between objects with ambient objects in a CAP category.
‣ EvaluatedGeneralizedEmbeddingInAmbientObject( gen ) | ( attribute ) |
The evaluation of the lazy generalized embedding gen.
‣ GeneralizedEmbeddingInAmbientObject( M ) | ( attribute ) |
Returns: a CAP generalized monomorphism
The generalized embedding of the object M into its ambient object.
‣ EmbeddingInAmbientObject( gen ) | ( attribute ) |
Returns: a CAP monomorphism
The embedding of the object M into its ambient object modulo the aid, i.e., the output is the associated monomorphism of the lazy generalized monomorphism gen with domain = identity.
‣ EmbeddingInAmbientObject( M ) | ( attribute ) |
‣ CreateLazyGeneralizedEmbeddingInAmbientObject( M, f, L ) | ( operation ) |
Construct a lazy evaluated generalized embedding with source M using the procedure f and the list of pre-arguments
L, which itself consists of pairs with first entry being a procedure and second its single argument. Use: CallFuncList( f, List( L, a -> a[1]( a[2] ) ) ). The input M is recovered by applying UnderlyingCell to the output. The list L should not include procedures which depend on their code-context, since otherwise GAP is forced to attach the code-context to the output.
‣ LazyGeneralizedEmbeddingInAmbientObject( M ) | ( operation ) |
The generalized embedding of the object M into its ambient object.
‣ ObjectWithAmbientObject( iota, A ) | ( operation ) |
Returns: an object in the category A with ambient objects
Construct an object in the category A with ambient objects out of the generalized embedding iota.
‣ ObjectWithAmbientObject( o, A ) | ( operation ) |
Returns: an object in the category A with ambient objects
Construct an object in the category A with ambient objects out of the identity morphism of o, view as a generalized embedding of o in itself.
‣ ObjectWithAmbientObjectFromLazyGeneralizedEmbedding( iota, A ) | ( operation ) |
Returns: an object in the category A with ambient objects
Construct an object in the category A with ambient objects out of the lazy generalized embedding iota.
‣ MorphismWithAmbientObject( phi, A ) | ( operation ) |
Returns: a morphism in the category A with ambient objects
‣ CategoryWithAmbientObjects( A ) | ( attribute ) |
Returns: a CAP category
‣ DisplayEmbeddingInAmbientObject( M ) | ( operation ) |
Returns: nothing
Display the embedding of the object M into its ambient object.
‣ WithAmbientObject( F, name, A, B ) | ( operation ) |
‣ WithAmbientObject( F, A, B ) | ( operation ) |
‣ WithAmbientObject( F, name, A ) | ( operation ) |
‣ WithAmbientObject( F, A ) | ( operation ) |
Returns: a CAP functor
Wrap the CAP functor F:UnderlyingCategory(A)\(\to\)UnderlyingCategory(B), where A and B are categories with ambient objects.
‣ WithAmbientObject( eta, name, F, G ) | ( operation ) |
‣ WithAmbientObject( eta, F, G ) | ( operation ) |
Returns: a CAP natural transformation
Wrap the CAP natural transformation eta:F!.UnderlyingFunctor\(\to\)G!.UnderlyingFunctor, where F and G are functors between categories with ambient objects.
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