# Kerodon

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Definition 8.5.3.5 (Split Idempotents). Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $F: \operatorname{N}_{\bullet }( \operatorname{Idem}) \rightarrow \operatorname{\mathcal{C}}$ be an idempotent in the $\infty$-category $\operatorname{\mathcal{C}}$. A splitting of $F$ is a functor $\overline{F}: \operatorname{N}_{\bullet }( \operatorname{Ret}) \rightarrow \operatorname{\mathcal{C}}$ satisfying $\overline{F}|_{ \operatorname{N}_{\bullet }( \operatorname{Idem}) } = F$. We say that $F$ is split if there exists a splitting of $F$.