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).