Remark 8.4.1.19 (Change of Target). Let $G: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be a functor of $\infty $-categories and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets. Then:
If $G$ is fully faithful and $G \circ F$ is dense, then $F$ is dense.
If $G$ is an equivalence of $\infty $-categories and $F$ is dense, then $G \circ F$ is dense.
See Remark 7.3.1.13.