双广群2-挠曲面的单纯解释
The simplicial interpretation of bigroupoid 2-torsors
摘要：
双范畴的行动作为范畴的行动的范畴化而产生。它们出现在各种不同的数学背景下，从Moerdijk在叶理理论中对正则李群胚的分类，到Waldmann在变形量子化方面的工作。对于任何这样的行动，我们引入一个行动bicategory，连同一个典型的投影（严格）2函子的bicategory的行为。当双范畴是一个双群胚时，我们可以在双范畴意义上附加作用是主作用的条件，从而产生一个双群胚2-torsor。在这种情况下，正则投影的Duskin神经恰好是Duskin-Glenn单纯2-torsor。
英文摘要：
Actions of bicategories arise as categorification of actions of categories. They appear in a variety of different contexts in mathematics, from Moerdijk's classification of regular Lie groupoids in foliation theory, to Waldmann's work on deformation quantization. For any such action we introduce an action bicategory, together with a canonical projection (strict) 2-functor to the bicategory which acts. When the bicategory is a bigroupoid, we can impose the additional condition that action is principal in bicategorical sense, giving rise to a bigroupoid 2-torsor. In that case, the Duskin nerve of the canonical projection is precisely the Duskin-Glenn simplicial 2-torsor.
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