Kerodon

Remark 7.3.3.4. In the situation of Definition 7.3.3.1, the morphism $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ is $U$-right Kan extended from $\operatorname{\mathcal{C}}^{0}$ if and only if the opposite functor $F^{\operatorname{op}}: \operatorname{\mathcal{C}}^{\operatorname{op}} \rightarrow \operatorname{\mathcal{D}}^{\operatorname{op}}$ is $U^{\operatorname{op}}$-left Kan extended from $(\operatorname{\mathcal{C}}^0)^{\operatorname{op}}$.