Proposition 4.1.5.10. Let $\operatorname{\mathcal{C}}$ be a category, and let $f: X \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ be a morphism of simplicial sets. Then $f$ is an inner covering map if and only if $X$ is isomorphic to the nerve of a category.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$