‣ SET_RANGE_CATEGORY_Of_HOMOMORPHISM_STRUCTURE ( C, H ) | ( operation ) |
The input are two categories C and H. There is not output but the following side effects are applied to C:
SetRangeCategoryOfHomomorphismStructure
( C, H )
SetIsEquippedWithHomomorphismStructure
( C, true
)
Furthermore, if IsCategoryWithDecidableLifts
( H ) then
SetIsCategoryWithDecidableLifts
( C, true
)
SetIsCategoryWithDecidableColifts
( C, true
)
An error is raised if RangeCategoryOfHomomorphismStructure
( C ) is already set.
‣ IsObjectFiniteCategory ( C ) | ( property ) |
Returns: true
or false
The (evil) property of C being a category with finitely many objects.
‣ IsFiniteCategory ( C ) | ( property ) |
Returns: true
or false
The (evil) property of C being a finite category.
‣ IsEquivalentToFiniteCategory ( C ) | ( property ) |
Returns: true
or false
The property of C being equivalent to a finite category.
‣ SetOfObjectsOfCategory ( C ) | ( attribute ) |
Returns: a list of CAP category objects
Return a duplicate free list of objects of the category C.
‣ SetOfObjects ( C ) | ( attribute ) |
Returns: a list of CAP category objects
Return a duplicate free list of objects of the category C. The corresponding CAP operation is SetOfObjectsOfCategory
.
‣ SetOfMorphismsOfFiniteCategory ( C ) | ( attribute ) |
Returns: a list of a CAP category morphisms
Return a duplicate free list of morphisms of the finite category C.
‣ SetOfMorphisms ( C ) | ( attribute ) |
Returns: a list of CAP category objects
Return a duplicate free list of morphisms of the finite category C. The corresponding CAP operation is SetOfMorphismsOfFiniteCategory
.
‣ CovariantHomFunctor ( o ) | ( attribute ) |
Returns: a CAP functor
The input is an object o in a category \(C\). The output is the covariant Hom functor \(\mathrm{Hom}\)(o,-) from the category \(C\) to RangeCategoryOfHomomorphismStructure
( C ).
‣ GlobalSectionFunctor ( C ) | ( attribute ) |
Returns: a CAP functor
Returns the global section functor \(\mathrm{Hom}(1,-)\) from the category C with terminal object \(1\) to RangeCategoryOfHomomorphismStructure
( C ).
‣ DatumOfCellAsEvaluatableString ( c, list_of_evaluatable_strings ) | ( operation ) |
Returns: a string
The arguments is a category cell c and a list list_of_evaluatable_strings of string all which must be evalutable with EvalString
. The output is a string str
such that
EvalString
( str
) = ObjectDatum( c ) if c is a category object, or
EvalString
( str
) = MorphismDatum( c ) if c is a category morphism.
The output string must, apart from the brackets, only consist of the substrings "ObjectConstructor
", "MorphismConstructor
" and the string in list_of_evaluatable_strings.
‣ CellAsEvaluatableString ( c, list_of_evaluatable_strings ) | ( operation ) |
Returns: a string
The arguments is a category cell c and a list list_of_evaluatable_strings of string all which must be evalutable with EvalString
. The output is a string str
such that
IsEqualForObjects( EvalString
( str
), c ) if c is a category object, or
IsEqualForMorphismsOnMor( EvalString
( str
), c ) if c is a category morphism.
The output string must, apart from the brackets, only consist of the substrings "ObjectConstructor
", "MorphismConstructor
" and the string in list_of_evaluatable_strings.
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