Corollary 9.2.3.10. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then $\operatorname{\mathcal{C}}$ is $\aleph _1$-cocomplete (that is, it admits countable colimits) if and only if it is finitely cocomplete and sequentially cocomplete. If these conditions are satisfied, then a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $\aleph _1$-cocontinuous (that is, it preserves countable colimits) if and only if it preserves finite colimits and sequential colimits.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$