Kerodon

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

Corollary 9.2.1.13. Let $\lambda $ be an uncountable regular cardinal. Then $\infty $-category $\operatorname{\mathcal{C}}$ admits $\lambda $-small filtered colimits if and only if it admits $\operatorname{N}_{\bullet }(A)$-indexed colimits, for every $\lambda $-small directed partially ordered set $(A, \leq )$.

Proof. Apply Proposition 9.2.1.11 in the special case $\kappa = \aleph _0$ (see Example 9.1.7.10). $\square$