Kerodon

Remark 9.1.9.18 (Monotonicity). Let $\kappa \leq \lambda $ be regular cardinals, and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits $\lambda $-small $\kappa $-filtered colimits. Then, for any regular cardinals $\kappa \leq \kappa ' \leq \lambda ' \leq \lambda $, the $\infty $-category $\operatorname{\mathcal{C}}$ also admits $\lambda '$-small, $\kappa '$-filtered colimits. Moreover, every $(\kappa ,\lambda )$-finitary functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is also $(\kappa ', \lambda ')$-finitary.