Kerodon

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

Corollary 9.2.2.20. Let $\lambda $ be a small regular cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits small filtered colimits. Then an object $C \in \operatorname{\mathcal{C}}$ is compact if and only if it both $(\aleph _0, \lambda )$-compact and $\lambda $-compact.