Kerodon

Corollary 9.2.2.30. Let $\kappa $ and $\lambda $ be small regular cardinals satisfying $\kappa \trianglelefteq \lambda $ and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits small $\kappa $-filtered colimits. 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.