Kerodon

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

Remark 4.5.3.4. Let $f: X \rightarrow Y$ be a categorical equivalence of simplicial sets. Then $f$ is a weak homotopy equivalence (since every Kan complex is an $\infty $-category). Beware that the converse is generally false.