Corollary 11.3.0.7. Let $q: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be an inner fibration of simplicial sets. Then $q$ is a locally cartesian fibration if and only if, for each edge $e: X \rightarrow Y$ of $\operatorname{\mathcal{D}}$, there exists a functor $\operatorname{\mathcal{C}}_{Y} \rightarrow \operatorname{\mathcal{C}}_{X}$ given by contravariant transport along $e$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$