Kerodon

Definition 9.1.9.3. Let $\kappa $ be a small regular cardinal, let $\operatorname{\mathcal{C}}$ be an $\infty $-category which admits small $\kappa $-filtered colimits, and let $\operatorname{\mathcal{D}}$ be another $\infty $-category. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $\kappa $-finitary if it preserves $\operatorname{\mathcal{K}}$-indexed colimits, for every small $\kappa $-filtered $\infty $-category $\operatorname{\mathcal{K}}$. We let $\operatorname{Fun}^{\kappa -\operatorname{fin}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the $\kappa $-finitary functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.