Kerodon

Remark 9.2.9.12. Let $\kappa \leq \lambda $ be regular cardinals and let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ be a $(\kappa ,\lambda )$-cocomplete inner fibration of simplicial sets. Then the $\infty $-category of sections $\operatorname{Fun}_{/\operatorname{\mathcal{C}}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{E}})$ is $(\kappa ,\lambda )$-cocomplete. Moreover, for every object $C \in \operatorname{\mathcal{C}}$, the evaluation functor $\operatorname{ev}_{C}: \operatorname{Fun}_{/\operatorname{\mathcal{C}}}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{E}}) \rightarrow \operatorname{Fun}_{ / \operatorname{\mathcal{C}}}( \{ C\} , \operatorname{\mathcal{E}}) = \operatorname{\mathcal{E}}_{C}$ is $(\kappa ,\lambda )$-finitary. By virtue of Remark 9.2.9.8, this is a special case of Corollary 7.1.10.4.