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Lie n-groupoids and stacky Lie groupoids

Chenchang Zhu
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Abstract

We discuss two sorts of generalization of Lie groupoids. One is Lie $n$-groupoids defined as simplicial manifolds with trivial $π_{k\geq n+1}$. The other is the stacky Lie groupoid $\cG\rra M$ with $\cG$ a differentiable stack. We build 1-1 correspondence between Lie 2-groupoids and stacky Lie groupoids up to a certain Morita equivalence. Equivalences of these higher groupoids are described.

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Chenchang Zhu. 2006-11-13. Lie n-groupoids and stacky Lie groupoids. https://arxiv.org/abs/math/0609420

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