Remark 4.5.4.2. Every categorical pushout square of simplicial sets is also a homotopy pushout square of simplicial sets (since every Kan complex $X$ is an $\infty $-category which satisfies $\operatorname{Fun}(K, X)^{\simeq } = \operatorname{Fun}(K, X)$ for every simplicial set $K$).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$