Vol. 298, No. 1, 2019

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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
Authors
Matías del Hoyo
Universidade Federal Fluminense
Niterói, RJ
Brazil
Davide Stefani
Université Pierre et Marie Curie
Place Jussieu
Paris
France