Kerodon

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

Example 7.7.3.10. Let $\operatorname{Kan}$ denote the category of Kan complexes. Then $\operatorname{Kan}$ is a cartesian closed category (Example 7.7.3.3), and carries a simplicial enrichment which satisfies the hypotheses of Remark 7.7.3.9. It follows that the $\infty $-category of spaces $\operatorname{\mathcal{S}}= \operatorname{N}_{\bullet }^{\operatorname{hc}}(\operatorname{Kan})$ is cartesian closed.