Kerodon

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

Theorem 9.1.5.7. Let $\operatorname{\mathcal{C}}$ be a small $\infty $-category and let $\kappa $ be a small infinite cardinal. Then $\operatorname{\mathcal{C}}$ is $\kappa $-filtered if and only if the colimit functor $\varinjlim : \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{S}}) \rightarrow \operatorname{\mathcal{S}}$ preserves $\kappa $-small limits.