n-Groupoids and Stacky Groupoids

By Chenchang Zhu. 2008

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We discuss two generalizations of Lie groupoids. One consists of Lie n-groupoids defined as simplicial manifolds with trivial π k≥ n+1 . The other consists of stacky Lie groupoids with 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 setup so that the statement is valid in both differential and topological categories. Hypercovers of higher groupoids in various categories are also described.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/c4fc9f6b7761728fc8a602255235e01efd77fc58