Kerodon

Definition 9.1.9.6. Let $\kappa \leq \lambda $ be regular cardinals and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits $\lambda $-small $\kappa $-filtered colimits. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $(\kappa ,\lambda )$-finitary if it preserves $\operatorname{\mathcal{K}}$-indexed colimits, for every $\infty $-category $\operatorname{\mathcal{K}}$ which is $\lambda $-small and $\kappa $-filtered. We let $\operatorname{Fun}^{(\kappa ,\lambda )-\operatorname{fin}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the $(\kappa ,\lambda )$-finitary functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.