Categorified groupoid-sets and their Burnside ring

Authors : Laiachi El KAOUTIT, Leonardo SPINOSA

Pages : 2069-2096

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Publication Date : 0000-00-00

Article Type : Research Paper

Abstract :We explore the category of internal categories in the usual category of insert ignore into journalissuearticles values(right); group-sets, whose objects are referred to as categorified group-sets. More precisely, we develop a new Burnside theory, where the equivalence relation between two categorified group-sets is given by a particular equivalence between the underlying categories. We also exhibit some of the differences between the old Burnside theory and the new one. Lastly, we briefly explain how to extend these new techniques and concepts to the context of groupoids, employing the categories of insert ignore into journalissuearticles values(right); groupoid-sets, aiming by this to give an alternative approach to the classical Burnside ring of groupoids.
Keywords : Internal categories, categorification, group actions, Burnside ring, double categories, groupoid actions