Dress’s theory of Mackey functors is a successful axiomatization of the representation theory of finite groups, capturing the formal aspects of such classical invariants as the character ring or group (co)homology. But, typically, each such invariant is only a partial shadow (consisting of abelian groups and homomorphisms) of a richer structure (consisting of additive, abelian or triangulated categories and suitable functors between them).
In joint work with Paul Balmer, we develop a theory of “Mackey 2-functors” in order to study this higher structure, thus explaining certain phenomena which, though invisible to classical Mackey functors, occur throughout equivariant mathematics.
In this talk I will provide examples of Mackey 2-functors, such as derived and stable module categories in representation theory or equivariant stable homotopy categories in topology, I will motivate our axioms and explain the first results of the theory.
For further details please refer to Group website