Definition 8.4.1.15. Let $\operatorname{\mathcal{D}}$ be an $\infty $-category and let $F: \operatorname{\mathcal{C}}\rightarrow \operatorname{\mathcal{D}}$ be a morphism of simplicial sets. We say that $F$ is dense if the identity transformation $\operatorname{id}_{F}: F \rightarrow \operatorname{id}_{\operatorname{\mathcal{D}}} \circ F$ exhibits the identity functor $\operatorname{id}_{\operatorname{\mathcal{D}}}$ as a left Kan extension of $F$ along $F$ (see Variant 7.3.1.5).
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