Goto Chapter: Top 1 2 Ind
 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 

1 Tools
 1.1 Tools
 1.2 Properties
 1.3 Attributes
 1.4 Functors
 1.5 Cell as evaluatable string

1 Tools

1.1 Tools

1.1-1 SET_RANGE_CATEGORY_Of_HOMOMORPHISM_STRUCTURE
‣ 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:

Furthermore, if IsCategoryWithDecidableLifts( H ) then

An error is raised if RangeCategoryOfHomomorphismStructure( C ) is already set.

1.2 Properties

1.2-1 IsObjectFiniteCategory
‣ IsObjectFiniteCategory( C )( property )

Returns: true or false

The (evil) property of C being a category with finitely many objects.

1.2-2 IsFiniteCategory
‣ IsFiniteCategory( C )( property )

Returns: true or false

The (evil) property of C being a finite category.

1.2-3 IsEquivalentToFiniteCategory
‣ IsEquivalentToFiniteCategory( C )( property )

Returns: true or false

The property of C being equivalent to a finite category.

1.3 Attributes

1.3-1 SetOfObjectsOfCategory
‣ SetOfObjectsOfCategory( C )( attribute )

Returns: a list of CAP category objects

Return a duplicate free list of objects of the category C.

1.3-2 SetOfObjects
‣ 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.

1.3-3 SetOfMorphismsOfFiniteCategory
‣ SetOfMorphismsOfFiniteCategory( C )( attribute )

Returns: a list of a CAP category morphisms

Return a duplicate free list of morphisms of the finite category C.

1.3-4 SetOfMorphisms
‣ 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.

1.4 Functors

1.4-1 CovariantHomFunctor
‣ 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 ).

1.4-2 GlobalSectionFunctor
‣ 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 ).

1.5 Cell as evaluatable string

1.5-1 DatumOfCellAsEvaluatableString
‣ 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

The output string must, apart from the brackets, only consist of the substrings "ObjectConstructor", "MorphismConstructor" and the string in list_of_evaluatable_strings.

1.5-2 CellAsEvaluatableString
‣ 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

The output string must, apart from the brackets, only consist of the substrings "ObjectConstructor", "MorphismConstructor" and the string in list_of_evaluatable_strings.

 [Top of Book]  [Contents]   [Previous Chapter]   [Next Chapter] 
Goto Chapter: Top 1 2 Ind

generated by GAPDoc2HTML