n-群胚与堆群胚
n-Groupoids and Stacky Groupoids
AI总结：
本文提出李n-群胚与堆李群胚两种推广，证明李2-群胚与堆李群胚在Morita等价下的一一对应，并推广到微分与拓扑范畴。
摘要：
我们讨论李群胚的两种推广。一种是由平凡π_{k≥n+1}的单纯流形定义的李n-群胚。另一种是堆李群胚cG↠M，其中cG是可微堆。我们在李2-群胚与堆李群胚之间建立了某种Morita等价意义下的一一对应。我们在一个一般性框架中证明这一点，使得该结论在微分和拓扑范畴中均成立。还描述了不同范畴中高阶群胚的等价性。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
