The general linear 2-groupoid

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.

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