Example 7.3.3.10. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $U: \operatorname{\mathcal{D}}\rightarrow \operatorname{\mathcal{E}}$ be a functor of $\infty $-categories. It follows from Proposition 7.3.3.7 that a functor $\overline{F}: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow \operatorname{\mathcal{D}}$ is a $U$-colimit diagram (in the sense of Definition 7.1.6.1) if and only if it is $U$-left Kan extended from $\operatorname{\mathcal{C}}$.
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