Remark 5.2.2.11. In the situation of Definition 5.2.2.10, we can identify $H$ and $\overline{H}$ with edges of the simplicial sets $\operatorname{Fun}(K, \operatorname{\mathcal{E}})$ and $\operatorname{Fun}(K, \operatorname{\mathcal{C}})$, respectively. Then $H$ is a $U$-cocartesian lift of $\overline{H}$ if and only if it is $U'$-cocartesian, where $U': \operatorname{Fun}(K,\operatorname{\mathcal{E}}) \rightarrow \operatorname{Fun}(K,\operatorname{\mathcal{C}})$ is given by postcomposition with $U$. (see Theorem 5.2.1.1).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$