Exercise 4.8.5.32. Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be functors of $\infty $-categories where $G$ is full and conservative. Show that if $G \circ F$ is essentially surjective, then $F$ is also essentially surjective. Beware that the hypothesis that $G$ is conservative cannot be omitted.
$\Newextarrow{\xhookrightarrow}{10,10}{0x21AA}$