Definition 7.7.1.21. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $K$ be a simplicial set. We say that a diagram $\mathscr {F}: K \rightarrow \operatorname{\mathcal{C}}$ has a universal colimit if there exists a universal colimit diagram $\overline{\mathscr {F}}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ satisfying $\overline{\mathscr {F}}|_{K} = \mathscr {F}$.
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