Remark 8.4.1.20. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets. Then $f$ is dense if and only if, for every object $Y \in \operatorname{\mathcal{D}}$, the composite map
\[ (\operatorname{\mathcal{C}}\times _{\operatorname{\mathcal{D}}} \operatorname{\mathcal{D}}_{/Y} )^{\triangleright } \rightarrow \operatorname{\mathcal{D}}_{/Y}^{\triangleright } \rightarrow \operatorname{\mathcal{D}} \]
is a colimit diagram in $\operatorname{\mathcal{D}}$.