Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 5.6.4.5. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a cocartesian fibration of simplicial sets. Then $U$ is an isofibration.

Proof. By virtue of Corollary 5.6.4.3, we may assume without loss of generality that $U$ is a cocartesian fibration of $\infty $-categories, in which case the desired result follows from Proposition 5.1.4.8. $\square$