On Burnside Theory for groupoids

Abstract

We explore the concept of conjugation between subgroupoids, providing several characterizations of the conjugacy relation (Theorem A in §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 §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.

The abstract and subsection 1.1 are changed; the title as well