Kerodon

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

Remark 5.4.5.5. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories. Then Theorem 4.6.6.5 supplies an equivalence of $\infty $-categories $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}}) \rightarrow \operatorname{Hom}^{\mathrm{L}}_{ \operatorname{ \pmb {\mathcal{QC}} }}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$. Beware that this equivalence is generally not an isomorphism at the level of simplicial sets.