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