Kerodon

$\Newextarrow{\xRightarrow}{5,5}{0x21D2}$ $\newcommand\empty{}$
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$

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.