  We show that the comma category $(\mathcal{F}\downarrow\mathbf{Grp})$ of
groups under the free group functor $\mathcal{F}: \mathbf{Set} \to
\mathbf{Grp}$ contains the category $\mathbf{Gph}$ of simple graphs as a full
coreflective subcategory. More broadly, we generalize the embedding of
topological spaces into Steven Vickers' category of topological systems to a
simple technique for embedding certain categories into comma categories, then
show as a straightforward application that simple graphs are coreflective in
$(\mathcal{F}\downarrow\mathbf{Grp})$.
