Algebra Seminar: Module categories via (co)monads and (bi)algebraic structures

Abstract: A module category is a category with an action of a monoidal category C. Often, C is a tensor category - in particular, it is rigid and abelian. In that case, C-module categories can be studied using modules over algebra objects in C.

In this talk, I will explain how certain monads on C generalize algebra objects, and can be used in the theory of C-module categories for C abelian but not rigid. Towards that end, I will first give a brief summary on monads and their Kleisli and Eilenberg-Moore categories.

If C=B-mod for a non-Hopf bialgebra B, I will show that the role of comodules for B-module coalgebras, associated to module categories in the Hopf case, is played by contramodules for bocses over B, with certain extra structure.

Join on site or via Zoom link (Meeting ID: 645 5572 6999, please contact the organizer for passcode)

This is a seminar in our algebra seminar series.