The general linear 2-groupoid
arXiv:1706.07152 · doi:10.2140/pjm.2019.298.33
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.
arXiv comment20 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
References in corpus (10)
- A 2-categories companion
- Integrating L-infinity algebras
- Vector bundles over Lie groupoids and algebroids
- Lie Groupoids and Differentiable Stacks
- VB-groupoids and representation theory of Lie groupoids
- From double Lie groupoids to local Lie 2-groupoids
- Deformations of Lie groupoids
- Morita equivalences of vector bundles
- n-Groupoids and Stacky Groupoids
- A Tannaka Theorem for Proper Lie Groupoids