Remark 4.6.2.17 (Transitivity). Let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ and $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be functors of $\infty $-categories, where $F$ is essentially surjective. Then $G$ is essentially surjective if and only if $G \circ F$ is essentially surjective. In particular, the collection of essentially surjective functors is closed under composition.

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