Kerodon

Corollary 9.2.3.11. Let $\kappa $ be a small regular cardinal and let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then $\operatorname{\mathcal{C}}$ admits small $\kappa $-filtered colimits if and only if it admits small $\kappa ^{+}$-filtered colimits and is $\kappa $-sequentially cocomplete. If these conditions are satisfied, then a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $\kappa $-finitary if and only if it is $\kappa ^{+}$-finitary and preserves $\kappa $-sequential colimits.