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arXiv · 0801.2057

n-Groupoids and Stacky Groupoids

Chenchang Zhu
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Abstract

We discuss two generalizations of Lie groupoids. One consists of Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. The other consists of stacky Lie groupoids $\cG\rra M$ with $\cG$ a differentiable stack. We build a 1-1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain Morita equivalence. We prove this in a general set-up so that the statement is valid in both differential and topological categories. \Equivalences of higher groupoids in various categories are also described.

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Chenchang Zhu. 2008-01-14. n-Groupoids and Stacky Groupoids. https://doi.org/10.1093/imrn%2Frnp080

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