n-Groupoids and Stacky Groupoids
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arXiv
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| Format: | Preprint |
| Publié: |
2008
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| _version_ | 1866909176381308928 |
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| author | Zhu, Chenchang |
| author_facet | Zhu, Chenchang |
| 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_0801_2057 |
| institution | arXiv |
| publishDate | 2008 |
| record_format | arxiv |
| spellingShingle | n-Groupoids and Stacky Groupoids Zhu, Chenchang Differential Geometry Category Theory 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. |
| title | n-Groupoids and Stacky Groupoids |
| topic | Differential Geometry Category Theory |
| url | https://arxiv.org/abs/0801.2057 |