Remark 8.5.3.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $F,F': \operatorname{N}_{\bullet }( \operatorname{Idem}) \rightarrow \operatorname{\mathcal{C}}$ be idempotents which are isomorphic (when regarded as objects of the $\infty $-category $\operatorname{Fun}( \operatorname{N}_{\bullet }( \operatorname{Idem}), \operatorname{\mathcal{C}})$). Then $F$ is split if and only if $F'$ is split. See Corollary 4.4.5.3.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$