# Kerodon

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Definition 8.5.7.1. Let $\operatorname{\mathcal{C}}$ be an $\infty$-category and let $e: X \rightarrow X$ be an endomorphism in $\operatorname{\mathcal{C}}$. We say that $e$ is homotopy idempotent if the homotopy class $[e]$ is an idempotent in the homotopy category $\mathrm{h} \mathit{\operatorname{\mathcal{C}}}$, in the sense of Definition 8.5.2.1.