Corollary 9.3.3.15. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $n$ be an integer, and let $Y$ be an $n$-truncated object of $\operatorname{\mathcal{C}}$. Then a morphism $f: X \rightarrow Y$ is $n$-truncated if and only if the object $X$ is $n$-truncated.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$