Remark 9.2.2.8 (Monotonicity). Let $\kappa \leq \lambda $ be regular cardinals, let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories. Assume that $\operatorname{\mathcal{C}}$ is $(\kappa ,\lambda )$-cocomplete and that $F$ is $(\kappa ,\lambda )$-finitary. Then the functor $F$ is also $(\kappa ',\lambda ')$-finitary, for any regular cardinals $\kappa \leq \kappa ' \leq \lambda ' \leq \lambda $ (compare with Remark 9.2.1.5).
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