Proposition 9.3.1.16. Let $\kappa \leq \lambda $ be regular cardinals and let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a right fibration of $\infty $-categories. Then there exists a categorical pullback diagram
where $h$ exhibits $\widehat{\operatorname{\mathcal{C}}}$ as an $\operatorname{Ind}_{\kappa }^{\lambda }$-completion of $\operatorname{\mathcal{C}}$, the $\infty $-category $\widehat{\operatorname{\mathcal{E}}}$ is $(\kappa ,\lambda )$-cocomplete, and $\widehat{U}$ is a $(\kappa ,\lambda )$-finitary right fibration. Moreover, for any diagram having these properties, the functor $\widetilde{h}$ exhibits $\widehat{\operatorname{\mathcal{E}}}$ as an $\operatorname{Ind}_{\kappa }^{\lambda }$-completion of $\widehat{\operatorname{\mathcal{E}}}$.