Corollary 8.5.9.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category containing an endomorphism $e: X \rightarrow X$. Then $e$ is homotopy idempotent if and only if there is a functor of $\infty $-categories $F: \operatorname{N}_{\bullet }^{\operatorname{D}}( B \mathrm{Dy} ) \rightarrow \operatorname{\mathcal{C}}$ satisfying $F( \overline{e} ) = e$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$