Corollary 9.2.3.10. Let $U: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a right fibration of $\infty $-categories, let $n$ be an integer, and let $f: X \rightarrow Y$ be a morphism of $\operatorname{\mathcal{C}}$. Then $f$ is $n$-truncated if and only if $U(f)$ is an $n$-truncated morphism of $\operatorname{\mathcal{D}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$