Warning 5.3.5.5. Let $\operatorname{\mathcal{C}}$ be a category and let $\mathscr {F}_0, \mathscr {F}_1: \operatorname{\mathcal{C}}\rightarrow \operatorname{QCat}$ be diagrams. The assumption that $\mathscr {F}_0$ is levelwise equivalent to $\mathscr {F}_1$ (in the sense of Definition 5.3.5.1) does not guarantee the existence of a levelwise categorical equivalence directly from $\mathscr {F}_0$ to $\mathscr {F}_1$ (or in the opposite direction).
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$