The general linear 2-groupoid
Differential Geometry
2020-05-05 v3 Algebraic Topology
Category Theory
Abstract
We deal with the symmetries of a (2-term) graded vector space or bundle. Our first theorem shows that they define a (strict) Lie 2-groupoid in a natural way. Our second theorem explores the construction of nerves for Lie 2-categories, showing that it yields simplicial manifolds if the 2-cells are invertible. Finally, our third and main theorem shows that smooth pseudofunctors into our general linear 2-groupoid classify 2-term representations up to homotopy of Lie groupoids.
Cite
@article{arxiv.1706.07152,
title = {The general linear 2-groupoid},
author = {Matias del Hoyo and Davide Stefani},
journal= {arXiv preprint arXiv:1706.07152},
year = {2020}
}
Comments
20 pages, updated version, an error on Proposition 5.4 pointed out by C. Zhu was fixed, Remark 5.6 was improved, some typos were corrected