Kerodon

Notation 7.6.6.5. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be $\infty $-categories. We let $\operatorname{Fun}^{\operatorname{\mathrm{cont}}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the continuous functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$, and $\operatorname{Fun}^{\operatorname{\mathrm{cocont}}}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ the full subcategory of $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$ spanned by the cocontinuous functors from $\operatorname{\mathcal{C}}$ to $\operatorname{\mathcal{D}}$.