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Strictification of étale stacky Lie groups

Part of: Families, fibrations Categories and geometry

Published online by Cambridge University Press:  30 November 2011

Giorgio Trentinaglia  and
Chenchang Zhu
Giorgio Trentinaglia
Affiliation:
Courant Research Centre ‘Higher Order Structures’, Georg-August-University Göttingen, Bunsenstrasse 3-5, 37073, Göttingen, Germany (email: gtrentin@uni-math.gwdg.de)
Chenchang Zhu
Affiliation:
Courant Research Centre ‘Higher Order Structures’, Georg-August-University Göttingen, Bunsenstrasse 3-5, 37073, Göttingen, Germany (email: zhu@uni-math.gwdg.de)
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Abstract

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We define stacky Lie groups to be group objects in the 2-category of differentiable stacks. We show that every connected and étale stacky Lie group is equivalent to a crossed module of the form (Γ,G) where Γ is the fundamental group of the given stacky Lie group and G is the connected and simply connected Lie group integrating the Lie algebra of the stacky group. Our result is closely related to a strictification result of Baez and Lauda.

Keywords

stacky Lie groupLie 2-groupcrossed modulesstrictificationcategorified group

MSC classification

Secondary: 18F99: None of the above, but in this section 14D23: Stacks and moduli problems
Type
Research Article
Information
Compositio Mathematica , Volume 148 , Issue 3 , May 2012 , pp. 807 - 834
Copyright
Copyright © Foundation Compositio Mathematica 2011

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