In the first part of the talk, we will discuss how bimodules (functors of the form G^{op} x G -> C)  can be used to provide a satisfactory theory of operadic structures. In particular, we show that this approach  has a natural analogue to the (Baez--Dolan) plus construction which leads to a convenient definition of so-called "algebras" over these operadic structures. We then describe some future work that builds upon this formalism and is motivated by the work of Connes and Kreimer. This includes showing that a particular kind of bimodule comonoid naturally admits a bialgebra structure and showing that B_+ operators have a natural formulation in terms of bimodule Hochschild cohomology.

Online Talk