Remark 4.8.5.13. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $n \geq -2$ be an integer. Then $\operatorname{\mathcal{C}}$ is locally $n$-truncated if and only if the projection map $\operatorname{\mathcal{C}}\rightarrow \Delta ^0$ is $m$-full for all $m \geq n+3$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$