The general linear 2-groupoid

Matías del Hoyo and Davide Stefani

Vol. 298 (2019), No. 1, 33–57

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.

Keywords

Lie 2-groupoids, nerve, simplicial manifolds, representation up to homotopy

Mathematical Subject Classification 2010

Primary: 18G30, 22A22, 57R22

Milestones

Received: 13 July 2017

Revised: 3 June 2018

Accepted: 4 June 2018

Published: 2 February 2019