Kerodon

Remark 7.4.2.5. We will see later that the equivalence $\mathrm{h} \mathit{ \operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{S}}) } \rightarrow \mathrm{h} \mathit{ \operatorname{LFib}( \operatorname{\mathcal{C}}) }$ of Theorem 7.4.2.4 can be upgraded to an equivalence of $\infty $-categories from $\operatorname{Fun}(\operatorname{\mathcal{C}}, \operatorname{\mathcal{S}})$ to the homotopy coherent nerve of $\operatorname{LFib}(\operatorname{\mathcal{C}})$. See Theorem .