Kerodon

Proposition 8.5.3.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\overline{F}: \operatorname{N}_{\bullet }( \operatorname{Ret}) \rightarrow \operatorname{\mathcal{C}}$ be a functor. Then $\overline{F}$ is both left and right Kan extended from the full subcategory $\operatorname{N}_{\bullet }( \operatorname{Idem}) \subset \operatorname{N}_{\bullet }( \operatorname{Ret})$.