Remark 5.5.1.5. Let $X$ and $Y$ be Kan complexes. Then Remark 4.6.8.6 supplies a canonical homotopy equivalence of Kan complexes $\operatorname{Fun}(X,Y) \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{S}}}( X,Y)$. Beware that this homotopy equivalence is generally not an isomorphism.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$