Kerodon

Remark 9.2.9.9. Let $\kappa \leq \lambda $ be regular cardinals and let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be an isofibration of $\infty $-categories. If the $\infty $-category $\operatorname{\mathcal{E}}$ is $(\kappa ,\lambda )$-cocomplete and the $U$ is a $(\kappa ,\lambda )$-finitary functor, then $U$ is $(\kappa ,\lambda )$-cocomplete as an inner fibration (Example 7.6.6.36). The converse holds if the $\infty $-category $\operatorname{\mathcal{C}}$ is $(\kappa ,\lambda )$-cocomplete and $U$ is a cocartesian fibration (Proposition 7.6.6.40).