Kerodon

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

Remark 4.4.3.22. Proposition 4.4.3.16 can be regarded as a special case of Proposition 4.4.3.21: it is equivalent to the assertion that, for every $\infty $-category $\operatorname{\mathcal{C}}$ and every Kan complex $X$, the canonical map $\operatorname{Fun}(X, \operatorname{\mathcal{C}}^{\simeq } ) \hookrightarrow \operatorname{Fun}( X, \operatorname{\mathcal{C}})^{\simeq }$ is bijective on vertices.