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Strictification of étale stacky Lie groups

Published online by Cambridge University Press:  30 November 2011

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

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.

Type
Research Article
Copyright
Copyright © Foundation Compositio Mathematica 2011

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