Remark 9.3.1.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n$ be an integer. Then $\operatorname{\mathcal{C}}$ is locally $n$-truncated (in the sense of Definition 4.8.2.1) if and only if every object $X \in \operatorname{\mathcal{C}}$ is $n$-truncated (in the sense of Definition 9.3.1.1).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$