nLab co-relation


This entry is about dual relations, un-related to correlation.



The notion of co-relations is the formal dual to that of relations, thus referring to jointly epimorphic cospans

XPY. X \longrightarrow P \longleftarrow Y \,.

In a category with coproducts, all co-relations factor through the coproduct of XX and YY. In fact, just as relations can be considered as subobjects of the Cartesian product, so corelations can be considered quotients of the coproduct (esp. when X+YPX+Y \to P is a regular epimorphism).


  • Brandon Coya and Brendan Fong, Corelations are the prop for extraspecial commutative Frobenius monoids, Theory and Applications of Categories 32 11 (2017) 380-395 [arxiv:1601.02307, tac:32-11]

Last revised on April 3, 2024 at 12:43:44. See the history of this page for a list of all contributions to it.