Topology Seminar: On Mackey 2-functors

(Joint work with Paul Balmer.) We propose a categorification of the notion of Mackey functor for finite groups, intended to capture "higher" equivariant phenomena occurring throughout mathematics which are invisible to ordinary Mackey functors. Examples of such structures include familiar equivariant objects such as: (abelian and derived) categories of linear group representations, stable module categories, equivariant topological spectra, equivariant KK-theory of C*-algebras, etc. Among the phenomena covered we find: ambidexterity (a.k.a. Wirthmüller isomophisms), the separable monadicity of restriction functors, block decompositions, etc.  In this talk I will motivate our axioms with examples and explain the first results of the theory.