Remark 8.4.1.17 (Homotopy Invariance). Let $\operatorname{\mathcal{D}}$ be an $\infty $-category, let $C$ be a simplicial set, and let $F,F': \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be diagrams which are isomorphic (when viewed as objects of the $\infty $-category $\operatorname{Fun}( \operatorname{\mathcal{C}}, \operatorname{\mathcal{D}})$). Then $F$ is dense if and only if $F'$ is dense. This follows by combining Remarks 7.3.1.11 and 7.3.1.12.
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