# Kerodon

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

Corollary 7.4.5.14. Let $\operatorname{\mathcal{C}}$ be a locally small $\infty$-category. For every object $X \in \operatorname{\mathcal{C}}$, the functors

$h^{X}: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{S}}\quad \quad h_{X}: \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{\mathcal{S}}$

preserve $K$-indexed limits, for every small simplicial set $K$.