Example 9.1.9.16. Let $\operatorname{QCat}$ denote the full subcategory of $\operatorname{Set_{\Delta }}$ spanned by the $\infty $-categories, and let $\operatorname{\mathcal{QC}}= \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{QCat})$ be its homotopy coherent nerve (see Construction 5.5.4.1). Then the inclusion functor
is finitary: this follows by combining Corollary 9.1.9.13 with Corollary 9.1.6.3. More generally, if $\lambda $ is an uncountable regular cardinal and $\operatorname{QCat}_{< \lambda }$ denote the category of $\lambda $-small $\infty $-categories, then the inclusion functor $\operatorname{N}_{\bullet }( \operatorname{QCat}_{< \lambda } ) \hookrightarrow \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{QCat}_{< \lambda } ) = \operatorname{\mathcal{QC}}_{< \lambda } )$ is $(\aleph _0, \lambda )$-finitary.