Definition 8.4.1.5. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category. We will say that a full subcategory $\operatorname{\mathcal{C}}\subseteq \operatorname{\mathcal{D}}$ is dense if, for every object $X \in \operatorname{\mathcal{D}}$, the composition
\[ ( \operatorname{\mathcal{C}}\times _{\operatorname{\mathcal{D}}} \operatorname{\mathcal{D}}_{/X} )^{\triangleright } \hookrightarrow \operatorname{\mathcal{D}}_{/X}^{\triangleright } \rightarrow \operatorname{\mathcal{D}} \]
is a colimit diagram.