Remark 5.5.1.4. Let $f: X \rightarrow Y$ be a morphism of Kan complexes. Then $f$ is a homotopy equivalence (in the sense of Definition 3.1.6.1) if and only if it is an isomorphism when viewed as a morphism of the $\infty $-category $\operatorname{\mathcal{S}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$