English

Generalized principal bundles and quotient stacks

Category Theory 2023-06-06 v2 Algebraic Geometry Algebraic Topology

Abstract

We consider the internalization of the usual notion of principal bundle in a site that has all pullbacks and a terminal object. We use this notion to consider the explicit construction of quotient prestacks via presheaves of categories of principal bundles equipped with equivariant morphisms in this abstract context. We then prove that, if the site is subcanonical and the underlying category satisfies some mild conditions, these quotient prestacks satisfy descent in the sense of stacks.

Keywords

Cite

@article{arxiv.2302.07852,
  title  = {Generalized principal bundles and quotient stacks},
  author = {Elena Caviglia},
  journal= {arXiv preprint arXiv:2302.07852},
  year   = {2023}
}

Comments

final version published in Theory and Applications of Categories

R2 v1 2026-06-28T08:41:02.930Z