Corollary 9.4.6.27. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a flat inner fibration of simplicial sets. Assume that, for each vertex $C \in \operatorname{\mathcal{C}}$, the $\infty $-category $\operatorname{\mathcal{E}}_{C}$ is idempotent complete. Then $U$ is an isofibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$