Example 9.2.2.5. Let $X$ be a Kan complex, which we view as an $\infty $-category in which every morphism is an isomorphism. Then $X$ admits small filtered colimits which are preserved by any functor of $\infty $-categories $X \rightarrow \operatorname{\mathcal{C}}$ (see Example 7.3.9.5). It follows that every vertex $x \in X$ is a compact object of $X$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$