Principal 2-bundles and quotient 2-stacks
Category Theory
2024-03-15 v1 Algebraic Geometry
Abstract
We generalize principal bundles and quotient stacks to the two-categorical context of bisites. We introduce a notion of principal 2-bundle that makes sense for a 2-category with finite flexible limits, endowed with a bitopology. We then use principal 2-bundles to explicitly construct quotient-pre-2-stacks, which are the analogues of quotient stacks one dimension higher. In order to perform this construction, we prove that principal 2-bundles are closed under iso-comma objects and we restrict ourselves to (2,1)-categories. Finally, we prove that, if the bisite is subcanonical and the underlying (2,1)-category satisfies some mild conditions, quotient pre-2-stacks are 2-stacks.
Cite
@article{arxiv.2403.09379,
title = {Principal 2-bundles and quotient 2-stacks},
author = {Elena Caviglia},
journal= {arXiv preprint arXiv:2403.09379},
year = {2024}
}