Definition:Graph Functor

Definition

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:

			Object functor:					$GX := X$
			Morphism functor:					$Gf := G_f$, the graph of $f$

Also see

• Graph Functor is Functor

Sources

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