Corollary 8.5.6.20. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category. Then the idempotent completion of $\operatorname{\mathcal{C}}$ has a final object if and only if there exists a right cofinal functor $\operatorname{N}_{\bullet }( \operatorname{Idem}) \rightarrow \operatorname{\mathcal{C}}$.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$