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| Main Author: | |
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| Format: | Preprint |
| Published: |
2008
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/0801.2057 |
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Table of Contents:
- We discuss two generalizations of Lie groupoids. One consists of Lie $n$-groupoids defined as simplicial manifolds with trivial $π_{k\geq n+1}$. 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.