Groupoid Actions on Sets, Duality and a Morita Context

2021/11/26 by Della Flora, Saradia, Flôres, Daiana, Morgado, Andrea +1
#FOS: Mathematics #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2111.13768

Abstract

Let G and K be groupoids. We present the notion of a (G_α,K_β)-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 isomorphism between the category of the left A-modules X-graded and the category of the left A #_α^GX-modules. As an application of this isomorphism, we construct a Morita context.

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