Kerodon

Corollary 9.2.9.7. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $\kappa \trianglelefteq \lambda \trianglelefteq \mu $ be regular cardinals, where $\lambda $ is uncountable. Then an object $X \in \operatorname{Ind}^{\mu }_{\kappa }(\operatorname{\mathcal{C}})$ is $(\lambda ,\mu )$-compact if and only if it belongs to the full subcategory $\operatorname{Ind}^{\lambda }_{\kappa }(\operatorname{\mathcal{C}})$ (see Remark 9.2.9.1).