Corollary 9.2.6.17. Let $\kappa $ be a small regular cardinal. Then the construction $\operatorname{\mathcal{C}}\mapsto \operatorname{Ind}_{\kappa }(\operatorname{\mathcal{C}})$ induces a bijection
\[ \xymatrix@R =50pt@C=50pt{ \{ \textnormal{Idempotent complete $\infty $-categories} \} / \textnormal{Equivalence} \ar [d]^{\sim } \\ \{ \textnormal{$\kappa $-compactly generated $\infty $-categories} \} / \textnormal{Equivalence}. } \]