Kerodon

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Proposition 5.3.4.17. Let $\mathscr {F}: \operatorname{\mathcal{C}}\rightarrow \operatorname{QCat}$ be a diagram of $\infty $-categories indexed by a category $\operatorname{\mathcal{C}}$. Then the morphism $\lambda _{t}: \underset { \longrightarrow }{\mathrm{holim}}( \mathscr {F} ) \rightarrow \operatorname{N}_{\bullet }^{\mathscr {F}}(\operatorname{\mathcal{C}})$ of Construction 5.3.4.11 is a scaffold of the cocartesian fibration $U: \operatorname{N}_{\bullet }^{\mathscr {F}}(\operatorname{\mathcal{C}}) \rightarrow \operatorname{N}_{\bullet }(\operatorname{\mathcal{C}})$.

Proof. Condition $(0)$ of Definition 5.3.4.2 follows from Remark 5.3.4.12, condition $(2)$ from Example 5.3.4.15, and condition $(1)$ from the characterization of $U$-cocartesian morphisms supplied by Proposition 5.3.3.15. $\square$