Orbifolds as stacks
Orbifolds as stacks
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Orbifolds 作为堆栈
DOI：
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发表时间：
2008
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通讯作者：
E. Lerman
中科院分区：
文献类型：
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作者：
E. Lerman
这篇综述论文的第一个目的是证明，如果orborold是群胚，那么orborold及其映射的集合必须被认为是一个2-范畴。将这与经典的萨塔克和瑟斯顿的定义进行比较，将其定义为具有额外结构的集合的1-范畴，和/或将其定义为直到Morita等价的适当的李群胚。
第二个目标是描述作为2-范畴的两种相辅相成的思维方式：
1.叶Lie群胚的弱2-范畴，双丛及双丛与双丛之间的等变映射
2.Deligne-Mumford的严格2-范畴堆叠在光滑流形范畴上。
The first goal of this survey paper is to argue that if orbifolds are groupoids, then the collection of orbifolds and their maps has to be thought of as a 2-category. Compare this with the classical definition of Satake and Thurston of orbifolds as a 1-category of sets with extra structure and/or with the "modern" definition of orbifolds as proper etale Lie groupoids up to Morita equivalence.
The second goal is to describe two complementary ways of thinking of orbifolds as a 2-category:
1. the weak 2-category of foliation Lie groupoids, bibundles and equivariant maps between bibundles and
2. the strict 2-category of Deligne-Mumford stacks over the category of smooth manifolds.