Warning 9.2.4.4. The notion of flat functor $\mathscr {F}: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{S}}$ introduced in Definition 9.2.4.1 is unrelated to the notion of flat inner fibration $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ introduced in Definition 8.7.6.1.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$