Kerodon

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

Corollary 9.2.1.17. Let $\lambda $ be a small regular cardinal. Then an $\infty $-category $\operatorname{\mathcal{C}}$ admits small filtered colimits if and only if it admits small $\lambda $-filtered colimits and $\lambda $-small filtered colimits.

Proof. Apply Corollary 9.2.1.16 in the special case $\kappa = \aleph _0$ (see Example 9.1.7.10). $\square$