Kerodon

Notation 9.2.5.7. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories. We let $\operatorname{Fun}^{\operatorname{lex}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the left exact functors $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$, and we let $\operatorname{Fun}^{\operatorname{rex}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the right exact functors $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$.