Kerodon

Corollary 5.3.5.8. Let $\operatorname{\mathcal{C}}$ be a category, let $U: \operatorname{\mathcal{E}}\rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$ be a cocartesian fibration of $\infty $-categories, and let $\operatorname{sTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}}$ denote the strict transport representation of Construction 5.3.1.5. Then the universal scaffold $\lambda _{u}: \underset { \longrightarrow }{\mathrm{holim}}( \operatorname{sTr}_{\operatorname{\mathcal{E}}/\operatorname{\mathcal{C}}} ) \rightarrow \operatorname{\mathcal{E}}$ of Construction 5.3.4.7 is a categorical equivalence of simplicial sets.