Variant 7.5.9.4. Let $\operatorname{\mathcal{C}}$ be a small filtered category. Then the inclusion map
\[ \operatorname{N}_{\bullet }( \operatorname{Kan}) \hookrightarrow \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Kan}) = \operatorname{\mathcal{S}} \]
preserves $\operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$-indexed colimits.