Pedro Brunialti Lima de Andrade (UVA): Bi-incomplete Tambara functors are almost never free

Abstract: In equivariant  homotopy theory, Mackey functors play the role of abelian (homotopy) groups and Tambara functors play the role of rings (algebras). In the category of abelian groups, free algebras are always free as abelian groups, however, in their work, Hill, Mehrle and Quigley show that free incomplete Tambara functors often fail to be free as Mackey functors. In this talk I will outline how this result extends to the case of bi-incmplete tambara functors, where now the underlying Mackey functor of the Tambara functor may also be incomplete. This is a joint work with Anna Marie Bohmann, Bertrand Guillou, David Mehrle and Chris Portwood.