# Kerodon

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

Remark 4.5.1.16. Let $X$ be an arbitrary simplicial set. Then the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{Fun}(X, \operatorname{\mathcal{C}})$ determines a functor from the homotopy category $\mathrm{h} \mathit{\operatorname{QCat}}$ to itself. In particular, if $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is an equivalence of $\infty$-categories, then the induced map $\operatorname{Fun}(X, \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}(X, \operatorname{\mathcal{D}})$ is also an equivalence of $\infty$-categories.