Kerodon

Warning 9.5.3.3. Let $\operatorname{\mathcal{C}}$ and $\operatorname{\mathcal{D}}$ be presentable $\infty $-categories. Every cocontinuous functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is automatically accessible, and can therefore be regarded as a morphism in the $\infty $-category $\operatorname{\mathcal{QC}}^{\operatorname{LPr}}$. However, a continuous functor $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ need not be accessible (see Warning 9.5.1.10), and therefore need not be a morphism in $\operatorname{\mathcal{QC}}^{\operatorname{RPr}}$.