‣ IsPosetCategory( C ) | ( property ) |
Returns: true or false
The property of C being a poset (category).
‣ IsTotalOrderCategory( C ) | ( property ) |
Returns: true or false
The property of C being a total order CAP category.
‣ IsMonoidalPoset( C ) | ( property ) |
Returns: true or false
The property of C being a monoidal thin skeletal category.
‣ IsClosedMonoidalPoset( C ) | ( property ) |
Returns: true or false
The property of C being a closed monoidal thin skeletal category.
‣ IsCoclosedMonoidalPoset( C ) | ( property ) |
Returns: true or false
The property of C being a coclosed monoidal thin skeletal category.
‣ IsSymmetricMonoidalPoset( C ) | ( property ) |
Returns: true or false
The property of C being a symmetric monoidal thin skeletal category.
‣ IsSymmetricClosedMonoidalPoset( C ) | ( property ) |
Returns: true or false
The property of C being a symmetric closed monoidal thin skeletal category.
‣ IsSymmetricCoclosedMonoidalPoset( C ) | ( property ) |
Returns: true or false
The property of C being a symmetric coclosed monoidal thin skeletal category.
‣ IsEqualForObjectsIfIsHomSetInhabited( A, B ) | ( operation ) |
Returns: true or false
Check if A is equal 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 partial order.
‣ AddIsEqualForObjectsIfIsHomSetInhabited( C, F ) | ( operation ) |
‣ AddIsEqualForObjectsIfIsHomSetInhabited( 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 IsEqualForObjectsIfIsHomSetInhabited. 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). \(F: ( arg2, arg3 ) \mapsto \mathtt{IsEqualForObjectsIfIsHomSetInhabited}(arg2, arg3)\).
Posets are skeletal, thin categories.
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