Corollary 8.5.8.8. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $e: X \rightarrow X$ be an endomorphism in $\operatorname{\mathcal{C}}$. Then $e$ is idempotent if and only if it can be extended to a diagram $\operatorname{N}_{\leq 3}( \operatorname{Idem}) \rightarrow \operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$