Corollary 4.6.4.24. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a right fibration of $\infty $-categories and let $F: K \rightarrow \operatorname{\mathcal{E}}$ be a diagram. Suppose that there exists an integer $n$ such that each fiber of $U$ is $n$-truncated and the simplicial set $K$ is $(n+1)$-connective. Then the map $U_{ /F}: \operatorname{\mathcal{E}}_{/F} \rightarrow \operatorname{\mathcal{C}}_{ / (U \circ F) }$ is a trivial Kan fibration.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$