Corollary 5.1.5.18. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a right fibration of $\infty $-categories and let $n \geq -2$ be an integer. Then $U$ is locally $n$-truncated if and only if, for every object $C \in \operatorname{\mathcal{C}}$, the Kan complex $\operatorname{\mathcal{E}}_{C}$ is $(n+1)$-truncated.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$