Corollary 9.2.7.5. Let $X$ be an essentially finite Kan complex. Then $X$ is compact when viewed as an object of the $\infty $-category $\operatorname{\mathcal{S}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$
Corollary 9.2.7.5. Let $X$ be an essentially finite Kan complex. Then $X$ is compact when viewed as an object of the $\infty $-category $\operatorname{\mathcal{S}}$.
Proof. Since the collection of compact objects of $\operatorname{\mathcal{S}}$ is closed under finite colimits (Corollary 9.2.2.23), this follows from the observation that $\Delta ^0 \in \operatorname{\mathcal{S}}$ is compact (Example 9.2.2.4). $\square$