Kerodon

Definition 9.2.4.7. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category and let $\kappa $ and $\lambda $ be regular cardinals, where $\lambda $ is uncountable. We say that a functor $\mathscr {F}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{S}}_{< \lambda }$ is $\kappa $-flat if the $\infty $-category of elements $\int _{\operatorname{\mathcal{D}}} \mathscr {F}$ is $\kappa $-cofiltered (Definition 9.1.1.4). We let $\operatorname{Fun}^{\kappa -\flat }( \operatorname{\mathcal{D}}, \operatorname{\mathcal{S}}_{< \lambda } )$ denote the full subcategory of $\operatorname{Fun}( \operatorname{\mathcal{D}}, \operatorname{\mathcal{S}}_{< \lambda } )$ spanned by those functors which are $\kappa $-flat.