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On two notions of a gerbe over a stack
Bulletin des Sciences Mathématiques ( IF 1.3 ) Pub Date : 2020-07-03 , DOI: 10.1016/j.bulsci.2020.102886
Saikat Chatterjee , Praphulla Koushik

Let G be a Lie groupoid. The category BG of principal G-bundles defines a differentiable stack. On the other hand, given a differentiable stack D, there exists a Lie groupoid H such that BH is isomorphic to D. Define a gerbe over a stack as a morphism of stacks F:DC, such that F and the diagonal map ΔF:DD×CD are epimorphisms. This paper explores the relationship between a gerbe defined above and a Morita equivalence class of a Lie groupoid extension.



中文翻译:

关于栈上的gerbe的两个概念

G成为李群怪。类别G 本金 G-bundles定义可区分的堆栈。另一方面,给定一个可微的堆栈d,存在一个李群 H 这样 H 同构 d。将堆栈上的gerbe定义为堆栈的态射FdC,如F和对角线图ΔFdd×Cd是种质。本文探讨了上面定义的gerbe和Lie groupoid扩展的Morita等价类之间的关系。

更新日期:2020-07-03
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