Corollary 7.2.5.10. Let $\operatorname{\mathcal{C}}$ be a locally Kan simplicial category. Then the $\infty $-category $\operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{\mathcal{C}})$ is filtered if and only if the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ is homotopy filtered, when regarded as an $\mathrm{h} \mathit{\operatorname{Kan}}$-enriched category.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$