2013/03/27 by Serge Bouc, Bouc, Serge
Mathematics · #Advanced Topics in Algebra #Advanced Topology and Set Theory #Category Theory (math.CT) #FOS: Mathematics #Group Theory (math.GR) #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.1303.6875
openalex publication_date 2013/03/27 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Let G be a finite group. In [HTW], Hambleton, Taylor and Williams have considered the question of comparing Mackey functors for G and biset functors defined on subgroups of G and bifree bisets as morphisms. This paper proposes a different approach to this problem, from the point of view of various categories of G-sets. In particular, the category of fused G-sets is introduced, as well its category of spans. The fused Mackey functors for G over a commutative ring R are defined as R-linear functors from this (R-linearized) category of spans to R-modules. They form an abelian subcategory of the category of Mackey functors for G over R, equivalent (for R=Z) to the category to the category of conjugation Mackey functors of [HTW]. The category of fused Mackey functors is also equivalent to the category of modules over the fused Mackey algebra, which is a quotient of the usual Mackey algebra of G over R. Reference: [HTW] I. Hambleton, L. R. Taylor, and E. B. Williams. Mackey functors and bisets. Geom. Dedicata, 148:157--174, 2010.