The simplicial interpretation of bigroupoid 2-torsors

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.