Rel, bicategory of relations, allegory
left and right euclidean;
extensional, well-founded relations.
By setoid objects one will means objects equipped with setoid-structure internal to suitable ambient categories. Setoid objects internal to Set are ordinary setoids.
Similarly to how the plain term setoids may refer to sets (objects of the category Set) equipped with either an equivalence relation or to sets equipped with a pseudo-equivalence relation, so the term setoid object in a finitely complete category may refer to either
an object quipped with an internal equivalence relation (i.e. a congruence)
an object equipped with an internal pseudo-equivalence relation.
Last revised on June 18, 2023 at 18:14:55. See the history of this page for a list of all contributions to it.