Remark 5.5.4.5. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories. Then Remark 4.6.8.6 supplies a homotopy equivalence of Kan complexes $\phi : \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})^{\simeq } \rightarrow \operatorname{Hom}_{\operatorname{\mathcal{QC}}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$. Beware that this homotopy equivalence is generally not an isomorphism.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$