Pullback of quantum principal bundles
Abstract
We introduce an abstract framework of Cartesian squares beyond the context of fiber products, and use it to extend the notion of pullback from classical to compact quantum principal bundles. Based only on our abstract notion of a Cartesian square, we extend key concepts of Equivariant Topology, such as the pullback of a family of group actions, orbit spaces, slices and global sections, change of base and structure group, free actions, and the groupoid of compact principal bundles. Finally, we embed the thus extended Equivariant Topology inside the 2-category of Grothendieck categories in such a way that our notion of a Cartesian square becomes the appropriate Beck-Chevalley condition.
Cite
@article{arxiv.2212.06946,
title = {Pullback of quantum principal bundles},
author = {Francesco D'Andrea and Tomasz Maszczyk},
journal= {arXiv preprint arXiv:2212.06946},
year = {2026}
}
Comments
v2: 52 pages. We split the paper in two parts. This is the first part about Cartesian squares. The second part about multiplicative K-theory will appear in a subsequent preprint