Abstract

For C a finite tensor category, Ostrik gave a complete description of C-module categories which can be reconstructed as categories of modules for an algebra object A in C. In other settings, interesting module categories can often be reconstructed as categories of modules for an algebra object in a larger monoidal category into which C embeds.In this talk, I will describe the category of Tambara modules on an arbitrary monoidal category C and explain how it can be viewed as the universal category for reconstructing algebra objects to live in. I will then present some applications of the Tambara formalism, based on ongoing joint work with Tony Zorman: an extension of Ostrik’s theorem to non-finite tensor categories, a characterization of exact module categories for finite tensor categories, and a reconstruction result for module categories over the non-rigid category B-comod, where B is a non-Hopf bialgebra.