Lie n-groupoids and stacky Lie groupoids

Details Lie n-groupoids and stacky Lie groupoids Lie n-groupoids and stacky Lie groupoids

2006-09-14

arxiv.org/abs/math/0609420v6

Mathematics

Differential Geometry

41pages, 10 figures, reference modified

Scientific paper

We discuss two sorts of generalization of Lie groupoids. One is Lie $n$-groupoids defined as simplicial manifolds with trivial $\pi_{k\geq n+1}$. 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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