Remark 9.1.6.5. We will see later that Corollary 9.1.6.3 and Variant 9.1.6.4 imply the a priori stronger assertion that the functors
\[ \operatorname{N}_{\bullet }( \operatorname{QCat}) \hookrightarrow \operatorname{\mathcal{QC}}\quad \quad \operatorname{N}_{\bullet }(\operatorname{Kan}) \hookrightarrow \operatorname{\mathcal{S}} \]
preserve colimits indexed by small filtered $\infty $-categories (see Examples 9.1.9.16 and 9.1.9.14).