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 $\mathbf{Set}$:

$\begin{xy} <0em,0em>*{E} = "E", <5em,0em>*{V} = "V", "E"+/^.3em/+/r1em/;"V"+/^.3em/+/l1em/ **@{-} ?>*@{>} ?*!/_.6em/{s}, "E"+/_.3em/+/r1em/;"V"+/_.3em/+/l1em/ **@{-} ?>*@{>} ?*!/^.6em/{t}, \end{xy}$

Sources

• 2010: Steve Awodey: Category Theory (2nd ed.) ... (previous) ... (next): $\S 1.7$