Definition 8.5.6.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. We say that an endomorphism $e: X \rightarrow X$ in $\operatorname{\mathcal{C}}$ is split idempotent if the homotopy class $[e]$ is a split idempotent in the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$ (see Example 8.5.2.3).
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