Definition 10.3.1.26. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $X$ be an object of $\operatorname{\mathcal{C}}$. We say that a sieve $\operatorname{\mathcal{C}}^{0}_{/X} \subseteq \operatorname{\mathcal{C}}_{/X}$ on $X$ is dense if the forgetful functor $\operatorname{\mathcal{C}}_{/X} \rightarrow \operatorname{\mathcal{C}}$ is left Kan extended from $\operatorname{\mathcal{C}}^{0}_{/X}$.
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