Strictification of étale stacky Lie groups (Q2894205)
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scientific article; zbMATH DE number 6051027
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Strictification of étale stacky Lie groups |
scientific article; zbMATH DE number 6051027 |
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Strictification of étale stacky Lie groups (English)
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29 June 2012
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stacky Lie group
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Lie \(2\)-group
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crossed module
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strictification
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categorified group
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differentiable stacks
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0.8834305
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0.8832091
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0.8828888
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0.88054156
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0.8793593
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A stacky Lie group, also called a Lie \(2\)-group, is a concept in higher group theory. Various definitions have been proposed. In this paper a stacky Lie group is defined to be a group object in the \(2\)-category of differentiable stacks; this is the same as a Lie \(2\)-group obtained from a Kan complex. The main result says that every connected and étale stacky Lie group is equivalent to a crossed module \((\Gamma,G)\), where \(\Gamma\) is the fundamental group and where \(G\)~is a connected and simply connected Lie group.
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