Research Seminar in Mathematics - Frobenius algebras and Grothendieck-Verdier categories
17 maj 2024 13:15 T213, Teknikhuset
Please contact Andrii Dmytryshyn if you have any questions regarding this seminar series.
Speaker
Jürgen Fuchs, Karlstad University.
Abstract
Traditionally one defines the structure of a Frobenius algebra as an associative algebra endowed with a non-degenerate invariant bilinear form. But several other definitions are possible; that these are equivalent can conveniently be understood with the help of a graphical calculus. Both the structures involved and this graphical calculus not only make sense in the realm of vector spaces, but for arbitrary monoidal categories. After giving some examples I will present a few results about Frobenius algebras in general monoidal categories. Then I will focus on a particular case, the so-called Grothendieck-Verdier categories, in which the tensor product is not an exact functor. Most of the required concepts and tools from category theory will be introduced along the way.
Welcome!