2024/03/02 by Raffael Stenzel, Stenzel, Raffael
Mathematics · #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Limits and Structures in Graph Theory #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2403.01167
openalex publication_date 2024/03/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We give a direct proof of the fact that Lurie's Unstraightening functor induces an equivalence between the strict (∞,2)-category of indexed quasi-categories and the strict (∞,2)-category of fibered quasi-categories over any given quasi-categorical base. We conclude that Unstraightening preserves simplicial cotensors up to a (strictly) natural homotopy equivalence, and thus gives rise to an accordingly weakened notion of cosmological biequivalence between the two underlying ∞-cosmoses.