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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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