Example 8.5.7.3. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $e: X \rightarrow X$ be an endomorphism in $\operatorname{\mathcal{C}}$. If $e$ is idempotent (that is, if it extends to a functor $\operatorname{N}_{\bullet }( \operatorname{Idem}) \rightarrow \operatorname{\mathcal{C}}$), then it is homotopy idempotent.
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