Turkish Journal of Mathematics
DOI
10.3906/mat-1811-63
Abstract
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.
Keywords
Internal categories, categorification, group actions, Burnside ring, double categories, groupoid actions
First Page
2069
Last Page
2096
Recommended Citation
KAOUTIT, LAIACHI EL and SPINOSA, LEONARDO
(2019)
"Categorified groupoid-sets and their Burnside ring,"
Turkish Journal of Mathematics: Vol. 43:
No.
5, Article 1.
https://doi.org/10.3906/mat-1811-63
Available at:
https://journals.tubitak.gov.tr/math/vol43/iss5/1
