\begin{definition}[Definition:Graph Functor]
Let $\mathbf{Set}$ and $\mathbf{Rel}$ be the category of sets and the category of relations, respectively.
The '''graph functor''' $G: \mathbf{Set} \to \mathbf{Rel}$ is defined by:
{{begin-axiom}}
{{axiom|lc= Object functor:
       |t = $GX := X$
}}
{{axiom|lc= Morphism functor:
       |t = $Gf := G_f$, the graph of $f$
}}
{{end-axiom}}
\end{definition}