Theorem 7.7.6.1. Let $\operatorname{\mathcal{C}}$ be a small simplicial set and let $\overline{\mathscr {F}}: \operatorname{\mathcal{C}}^{\triangleright } \rightarrow \operatorname{\mathcal{S}}$ be a colimit diagram. Then $\overline{\mathscr {F}}$ is a strongly universal colimit diagram.
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