Corollary 9.3.1.15. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category, let $n$ be an integer, and let $X$ be an $(n-1)$-truncated object of $\operatorname{\mathcal{C}}$. Then the canonical map $\mathrm{h}_{\mathit{\leq n}}\mathit{(\operatorname{\mathcal{C}}_{/X} )} \rightarrow \mathrm{h}_{\mathit{\leq n}}\mathit{(\operatorname{\mathcal{C}})}_{/X}$ is an equivalence of $\infty $-categories.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$