Definition 7.7.1.15. Let $\operatorname{\mathcal{C}}$ be an $\infty $-category and let $K$ be a simplicial set. We say that a morphism $\overline{\mathscr {F}}: K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a universal colimit diagram if, for every cartesian natural transformation $\overline{\mathscr {F}}' \rightarrow \overline{\mathscr {F}}$, the morphism $\overline{\mathscr {F}}': K^{\triangleright } \rightarrow \operatorname{\mathcal{C}}$ is a colimit diagram in the $\infty $-category $\operatorname{\mathcal{C}}$.
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