Corollary 9.3.1.21. Let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a right fibration of $\infty $-categories, let $n$ be an integer such that every fiber of $U$ is $n$-truncated, and let $K$ be an $(n+1)$-connective simplicial set. Then a morphism $\overline{F}: K^{\triangleleft } \rightarrow \operatorname{\mathcal{E}}$ is a limit diagram in $\operatorname{\mathcal{E}}$ if and only if $U \circ \overline{F}$ is a limit diagram in $\operatorname{\mathcal{C}}$. In particular, the functor $U$ preserves $K$-indexed limits.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$