# Kerodon

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

Corollary 4.4.4.6. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category. Then the functor

$(\operatorname{Set_{\Delta }})^{\operatorname{op}} \rightarrow \operatorname{Set_{\Delta }}\quad \quad X \mapsto \operatorname{Fun}(X, \operatorname{\mathcal{C}})^{\simeq }$

preserves limits (that is, it carries colimits in the category of simplicial sets to limits of Kan complexes).