Colimits in the $\infty$-category of $\infty$-topoi and \'etale morphisms
Category Theory
2025-06-13 v1 Algebraic Topology
Abstract
We provide an alternative proof of Lurie's result that the wide subcategory of the -category of -topoi spanned by the \'etale morphisms is closed under small colimits. Our proof is based on a new characterization of \'etale 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.
Cite
@article{arxiv.2506.10431,
title = {Colimits in the $\infty$-category of $\infty$-topoi and \'etale morphisms},
author = {Taichi Uemura},
journal= {arXiv preprint arXiv:2506.10431},
year = {2025}
}