2018/07/12 by Laiachi El Kaoutit, Kaoutit, Laiachi El, Leonardo Spinosa +1 · 1 citation
Mathematics · #18B40 #19A22 #20L05 #Algebraic structures and combinatorial models #Category Theory (math.CT) #Commutative Algebra (math.AC) #FOS: Mathematics #Geometric and Algebraic Topology #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology
paper · pdf · doi:10.48550/arxiv.1807.04470
openalex publication_date 2018/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.