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 $\operatorname{\mathcal{C}}$-indexed colimits commute with $\kappa $-small limits in the $\infty $-category of spaces $\operatorname{\mathcal{S}}$.