Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Example 9.2.2.4. The Kan complex $\Delta ^0$ corepresents the identity functor $\operatorname{id}: \operatorname{\mathcal{S}}\rightarrow \operatorname{\mathcal{S}}$ (see Proposition 5.6.6.17), and is therefore compact when viewed as an object of the $\infty $-category of spaces $\operatorname{\mathcal{S}}$. See Corollary 9.2.7.5 for a more general statement.