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The general linear
2-groupoid
Matías del Hoyo and Davide Stefani |
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Vol. 298 (2019), No. 1, 33–57
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DOI: 10.2140/pjm.2019.298.33
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Abstract |
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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. |
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Keywords
Lie 2-groupoids, nerve, simplicial manifolds,
representation up to homotopy
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Mathematical Subject Classification 2010
Primary: 18G30, 22A22, 57R22
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Milestones
Received: 13 July 2017
Revised: 3 June 2018
Accepted: 4 June 2018
Published: 2 February 2019
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Authors |
| Matías del Hoyo | |
| Universidade Federal
Fluminense Niterói, RJ Brazil |
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| Davide Stefani | |
| Université Pierre et Marie
Curie Place Jussieu Paris France |
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