Proposition 9.4.1.18. Let $\kappa \leq \lambda $ be regular cardinals, where $\lambda $ is uncountable. Then the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{Ind}_{\kappa }^{\lambda }(\operatorname{\mathcal{C}})$ induces a bijection
\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Idempotent-complete $\infty $-categories} \} / \textnormal{Equivalence} \ar [d]^{\sim } \\ \{ \textnormal{$(\kappa ,\lambda )$-compactly generated $\infty $-categories} \} / \textnormal{Equivalence}. } \]