nLab co-relation

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

---

Idea

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

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

In a category with coproducts, all co-relations factor through the coproduct of $X$ and $Y$. 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 $X+Y \to P$ is a regular epimorphism).

References

• 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]