On Burnside Theory for groupoids
Group Theory
2021-06-29 v2 Commutative Algebra
Category Theory
Abstract
We explore the concept of conjugation between subgroupoids, providing several characterizations of the conjugacy relation (Theorem A in {\S}1.2). We show that two finite groupoid-sets, over a locally strongly finite groupoid, are isomorphic, if and only if, they have the same number of fixed points with respect to any subgroupoid with a single object (Theorem B in {\S}1.2). Lastly, we examine the ghost map of a finite groupoid and the idempotents elements of its Burnside algebra. The exposition includes an Appendix where we gather the main general technical notions that are needed along the paper.
Cite
@article{arxiv.1807.04470,
title = {On Burnside Theory for groupoids},
author = {Laiachi El Kaoutit and Leonardo Spinosa},
journal= {arXiv preprint arXiv:1807.04470},
year = {2021}
}
Comments
The abstract and subsection 1.1 are changed; the title as well