Kerodon

Remark 7.3.1.6. In the situation of Variant 7.3.1.5, the natural transformation $\beta : F_0 \rightarrow F \circ \delta $ exhibits $F$ as a left Kan extension of $F_0$ along $\delta $ if and only if it exhibits $F^{\operatorname{op}}$ as a right Kan extension of $F_0^{\operatorname{op}}$ along $\delta ^{\operatorname{op}}$, when regarded as a morphism in the $\infty $-category $\operatorname{Fun}(K^{\operatorname{op}}, \operatorname{\mathcal{D}}^{\operatorname{op}}) \simeq \operatorname{Fun}(K, \operatorname{\mathcal{D}})^{\operatorname{op}}$.