Corollary 9.1.2.9. 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.
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