Remark 4.8.6.6 (Monotonicity). Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a functor of $\infty $-categories and let $m \leq n$ be integers. If $F$ is essentially $m$-categorical, then it is essentially $n$-categorical.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$