2025/06/12 by Taichi Uemura, Uemura, Taichi
Mathematics · #Homotopy and Cohomology in Algebraic Topology #Algebraic structures and combinatorial models #Advanced Topology and Set Theory
paper · pdf · doi:10.48550/arxiv.2506.10431
We provide an alternative proof of Lurie's result that the wide subcategory of the ∞-category of ∞-topoi spanned by the étale morphisms is closed under small colimits. Our proof is based on a new characterization of étale morphisms of ∞-topoi in relation to univalent families and does not rely on a larger universe. During the proof, we also give an elementary construction of univalent completion.