Definition:Inverse Relation Functor

Definition
Let $\mathbf{Rel}$ be the category of relations.

The inverse relation (contravariant) functor $C: \mathbf{Rel} \to \mathbf{Rel}$ is the contravariant functor defined by:

That it is in fact a contravariant functor is shown on Inverse Relation Functor is Contravariant Functor.