Mackey functors and bisets
arXiv:0806.4054
Abstract
For any finite group G, we define a bivariant functor from the Dress category of finite G-sets to the conjugation biset category, whose objects are subgroups of G, and whose morphisms are generated by certain bifree bisets. Any additive functor from the conjugation biset category to abelian groups yields a Mackey functor by composition. We characterize the Mackey functors which arise in this way.
Remark 1.1 on the literature expanded, following a referee's report. Final version: to appear in Geometria Dedicata