Remark 11.3.0.12. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a functor between categories. Then a cleavage of $U$ exists if and only if $U$ is a locally cartesian fibration (Definition 11.10.3.8).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$