Remark 4.8.6.8. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be functors of $\infty $-categories and let $n$ be an integer. Suppose that $G$ is essentially $n$-categorical. Then $F$ is essentially $n$-categorical if and only if $G \circ F$ is essentially $n$-categorical. This follows by combining Remarks 4.8.6.6 and 4.8.6.7.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$