On Burnside Theory for groupoids El Kaoutit Zerri, Laiachi Spinosa, Leonardo We explore the concept of conjugation between subgroupoids, providing several characteriza- tions 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. 2025-01-08T08:06:06Z 2025-01-08T08:06:06Z 2023 journal article 1220-3874 https://hdl.handle.net/10481/98617 eng http://creativecommons.org/licenses/by-nc-nd/4.0/ open access Attribution-NonCommercial-NoDerivatives 4.0 Internacional BULLETIN MATHÉMATIQUE de la Société des Sciences Mathématiques de Roumanie (Bull. Math. Soc. Sci. Math. Roumanie)