Kerodon

Definition 9.1.9.1. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories, where $\operatorname{\mathcal{C}}$ admits small filtered colimits. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is finitary if $F$ preserves $\operatorname{\mathcal{K}}$-indexed colimits, for every small filtered $\infty $-category $\operatorname{\mathcal{K}}$. We let $\operatorname{Fun}^{\operatorname{fin}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the finitary functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.