Example 5.2.2.6. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a left covering map of simplicial sets. Then, for every edge $f: C \rightarrow D$ in $\operatorname{\mathcal{C}}$, there is a unique functor $\operatorname{\mathcal{E}}_{C} \rightarrow \operatorname{\mathcal{E}}_{D}$ given by covariant transport along $f$, which can be identified with the covariant transport function given by Construction 5.2.0.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$