  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.
