Corollary 7.5.9.6. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category which admits finite colimits and small filtered colimits. Then $\operatorname{\mathcal{D}}$ admits all small colimits. Moreover, if $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ is a functor of $\infty $-categories which preserves finite colimits and small filtered colimits, then $G$ preserves all small colimits.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Proof. This is a special case of Corollary 7.5.9.5, since every small simplicial set $K$ can be realized as a (small) filtered colimit of finite simplicial sets. For example, we can write $K$ as the union of all finite simplicial subsets of itself. $\square$