Warning 4.2.2.2. The requirement that a functor $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{\mathcal{C}}$ is a fibration in groupoids is not invariant under equivalence. For example, an equivalence of categories need not be a fibration in groupoids.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$