‣ InfoLocales | ( info class ) |
‣ UniqueMorphism( A, B ) | ( operation ) |
Returns: a CAP morphism
Construct the unique morphism with source A and target B.
‣ IsThinCategory( C ) | ( property ) |
Returns: true or false
The property of C being a thin CAP category.
‣ IsDiscreteCategory( C ) | ( property ) |
Returns: true or false
The property of C being a discrete CAP category, i.e., equivalent to a category in which any morphism is an identity.
‣ IsMonoidalProset( C ) | ( property ) |
Returns: true or false
The property of C being a monoidal thin category.
‣ IsClosedMonoidalProset( C ) | ( property ) |
Returns: true or false
The property of C being a closed monoidal thin category.
‣ IsCoclosedMonoidalProset( C ) | ( property ) |
Returns: true or false
The property of C being a coclosed monoidal thin category.
‣ IsSymmetricMonoidalProset( C ) | ( property ) |
Returns: true or false
The property of C being a symmetric monoidal thin category.
‣ IsSymmetricClosedMonoidalProset( C ) | ( property ) |
Returns: true or false
The property of C being a symmetric closed monoidal thin category.
‣ IsSymmetricCoclosedMonoidalProset( C ) | ( property ) |
Returns: true or false
The property of C being a symmetric coclosed monoidal thin category.
‣ AreIsomorphicForObjectsIfIsHomSetInhabited( A, B ) | ( operation ) |
Returns: true or false
Check if A is isomorphic to B under the assumption that there exists a morphism from A to B, i.e., if A is known to be less or equal to B w.r.t. the preorder.
‣ IsCategoryWithoutMorphismData( object ) | ( filter ) |
Returns: true or false
The GAP category of categories with morphisms without a morphism datum.
‣ IsObjectInThinCategory( object ) | ( filter ) |
Returns: true or false
The GAP category of objects in a thin CAP category.
‣ IsMorphismInThinCategory( morphism ) | ( filter ) |
Returns: true or false
The GAP category of morphisms in a thin CAP category.
‣ AddAreIsomorphicForObjectsIfIsHomSetInhabited( C, F ) | ( operation ) |
‣ AddAreIsomorphicForObjectsIfIsHomSetInhabited( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation AreIsomorphicForObjectsIfIsHomSetInhabited. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( arg2, arg3 ) \mapsto \mathtt{AreIsomorphicForObjectsIfIsHomSetInhabited}(arg2, arg3)\).
‣ AddUniqueMorphism( C, F ) | ( operation ) |
‣ AddUniqueMorphism( C, F, weight ) | ( operation ) |
Returns: nothing
The arguments are a category \(C\) and a function \(F\). This operation adds the given function \(F\) to the category for the basic operation UniqueMorphism. Optionally, a weight (default: 100) can be specified which should roughly correspond to the computational complexity of the function (lower weight = less complex = faster execution). \(F: ( A, B ) \mapsto \mathtt{UniqueMorphism}(A, B)\).
Prosets are thin categories, i.e., each Hom-set is either a singleton or empty.
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