Corollary 7.4.5.17. 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 $K$.