Definition:Directed Graph/Category-Theoretic Definition

Definition
Let $\mathbf {Set}$ be the category of sets.

A digraph is an arrangement of the following form in $\mathbf{Set}$:


 * $\begin{xy}

<0em,0em>*{E} = "E", <5em,0em>*{V} = "V",

"E"+/^.3em/+/r1em/;"V"+/^.3em/+/l1em/ **@{-} ?>*@{>} ?*!/_.6em/{s}, "E"+/_.3em/+/r1em/;"V"+/_.3em/+/l1em/ **@{-} ?>*@{>} ?*!/^.6em/{t}, \end{xy}$