Kerodon

Corollary 9.1.9.20. Let $\kappa $ and $\lambda $ be small regular cardinals satisfying $\kappa \trianglelefteq \lambda $. Then an $\infty $-category $\operatorname{\mathcal{C}}$ admits small $\kappa $-filtered colimits if and only if it admits small $\lambda $-filtered colimits and $\lambda $-small $\kappa $-filtered colimits. 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 both $\lambda $-finitary and $(\kappa , \lambda )$-finitary.