Kerodon

Definition 9.4.2.1. Let $\operatorname{\mathcal{C}}$ be a compactly generated $\infty $-category and let $\operatorname{\mathcal{D}}$ be an $\infty $-category which admits small filtered colimits. We say that a functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is compact if it is finitary (Definition 9.2.2.1) and carries compact objects of $\operatorname{\mathcal{C}}$ to compact objects of $\operatorname{\mathcal{D}}$. We let $\operatorname{Fun}^{\operatorname{c}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the compact functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.