Categorified groupoid-sets and their Burnside ring El Kaoutit Zerri, Laiachi Spinosa, Leonardo We explore the category of internal categories in the usual category of (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 (right) groupoid-sets, aiming by this to give an alternative approach to the classical Burnside ring of groupoids 2025-01-08T08:07:20Z 2025-01-08T08:07:20Z 2019 journal article https://hdl.handle.net/10481/98618 10.3906/mat-1811-63 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional Turkish Journal of Mathematics