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arXiv · 1012.4103

From double Lie groupoids to local Lie 2-groupoids

Rajan Amit Mehta·Xiang Tang
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Abstract

We apply the bar construction to the nerve of a double Lie groupoid to obtain a local Lie 2-groupoid. As an application, we recover Haefliger's fundamental groupoid from the fundamental double groupoid of a Lie groupoid. In the case of a symplectic double groupoid, we study the induced closed 2-form on the associated local Lie 2-groupoid, which leads us to propose a definition of a symplectic 2-groupoid.

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Rajan Amit Mehta, Xiang Tang. 2010-12-18. From double Lie groupoids to local Lie 2-groupoids. https://doi.org/10.1007/s00574-011-0033-4

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