Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

Corollary 7.4.5.12. Let $\operatorname{\mathcal{C}}$ be an $\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 simplicial set $K$.