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Groupoid actions on sets, duality and a morita context

Groupoid actions on sets, duality and a morita context

Let G and K be groupoids. We present the notion of a (Gα,Kβ)-set and we prove a duality theorem in this context, which extends the duality theorem for graded algebras by groups. For A a unital G-graded algebra and X a finite split G-set, we show that there is an …