Example 9.1.9.14. Let $\operatorname{Kan}$ denote the ordinary category of Kan complexes and let $\operatorname{\mathcal{S}}$ denote the $\infty $-category of spaces. Then the inclusion functor
is finitary: this follows by combining Corollary 9.1.9.13 with Variant 9.1.6.4. More generally, if $\lambda $ is an uncountable regular cardinal and $\operatorname{Kan}_{< \lambda }$ denote the category of $\lambda $-small Kan complexes, then the inclusion functor $\operatorname{N}_{\bullet }( \operatorname{Kan}_{< \lambda } ) \hookrightarrow \operatorname{N}_{\bullet }^{\operatorname{hc}}( \operatorname{Kan}_{< \lambda } ) = \operatorname{\mathcal{S}}_{< \lambda } )$ is $(\aleph _0, \lambda )$-finitary: that is, it preserves $\lambda $-small filtered colimits.