Corollary 9.2.6.15. Let $\kappa \leq \lambda $ be regular cardinals and let $\operatorname{\mathcal{C}}$ be an $\infty $-category which is idempotent complete. Then the tautological map $\operatorname{\mathcal{C}}\rightarrow \operatorname{Ind}_{\kappa }^{\lambda }(\operatorname{\mathcal{C}})$ induces an equivalence from $\operatorname{\mathcal{C}}$ to the full subcategory of $\operatorname{Ind}_{\kappa }^{\lambda }(\operatorname{\mathcal{C}})$ spanned by the $(\kappa ,\lambda )$-compact objects.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$