Definition 9.2.4.1. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category. We say that a functor $\mathscr {F}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{S}}$ is flat if if the $\infty $-category of elements $\int _{\operatorname{\mathcal{D}}} \mathscr {F}$ is cofiltered (see Definition 5.6.2.1). We let $\operatorname{Fun}^{\flat }(\operatorname{\mathcal{D}}, \operatorname{\mathcal{S}})$ denote the full subcategory of $\operatorname{Fun}(\operatorname{\mathcal{D}}, \operatorname{\mathcal{S}})$ spanned by the flat functors.
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