Corollary 8.5.3.10 (Uniqueness of Splittings). Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the restriction functor
\[ \operatorname{Fun}( \operatorname{N}_{\bullet }( \operatorname{Ret}), \operatorname{\mathcal{C}}) \rightarrow \operatorname{Fun}( \operatorname{N}_{\bullet }( \operatorname{Idem}), \operatorname{\mathcal{C}}) \]
is fully faithful, and its essential image is the full subcategory consists of the split idempotents in $\operatorname{\mathcal{C}}$.