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:

			Object functor:					$CX := X$
			Morphism functor:					$C \RR := \RR^{-1}$, the inverse relation to $\RR$

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

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.9$: Exercise $1 \,\text{(c)}$