\begin{definition}[Definition:Inverse Relation Functor]
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:
{{begin-axiom}}
{{axiom|lc= Object functor:
       |t = $CX := X$
}}
{{axiom|lc= Morphism functor:
       |t = $C \RR := \RR^{-1}$, the inverse relation to $\RR$
}}
{{end-axiom}}
That it is in fact a contravariant functor is shown on Inverse Relation Functor is Contravariant Functor.
\end{definition}