| Résume | Let us consider 6 operations related to finite groups: Ind, Res, Jnd, and Inf, Def(=Orb) Inv. Functorially, these are dealt with by the following notions. (1) Mackey functor: Ind and Res. (2) Biset functor: Ind, Res, Inf and Def. (3) Tambara functor: Ind, Res, Jnd.
One possible way to deal with all of 6, would be to consider some 'Tambara structure' for a biset functor.
In this talk, for this purpose, I will introduce the 2-category $\mathbb{S}$ of finite sets with variable finite group actions, whose 2-fibered products allows us to define Mackey functors on it. With this definition, biset functors can be regarded as a special kind of Mackey functors on $\mathbb{S}$.
If the time permits, I will also attach a system of adjoint triplets to $\mathbb{S}$ satisfying analogous properties to a derivator, and explain how the associated Burnside biset functor has a partial Tambara structure. |
