Wednesday 18 April 2012 h. 15:00, room 2BC30

Isar GOYVAERTS (Vrije Universiteit Brussel)

"A glimpse of categorical algebra"

*-Abstract*

Category theory occupies a central position in contemporary mathematics and theoretical computer science, and occurs as well in other areas such as mathematical physics and linguistics. Roughly speaking, it provides a general abstract theory of structures and of systems of structures.

The study of categories is an attempt to axiomatically capture what is commonly found in various classes of related mathematical structures.

A way of thinking about category theory is that it is a refinement (or "categorification") of ordinary algebra.

In this talk, we will focus on the notion of a monoidal category, i.e. the categorification of the notion of a monoid.

Monoidal categories have numerous applications outside of category theory itself and provide a tool to connect a priori quite remote branches of mathematics.

We start the talk with some basic notions and definitions and provide some examples. Next, we try to sketch the idea of doing "categorical algebra" by considering a concrete example in more detail. We finish the talk with mentioning some recent results and some of the type of problems we are interested in.

No specific knowledge of category theory is required. The only prerequisites is some notion of the basic definitions in the theory of certain algebraic structures (such as monoids, groups and vector spaces).

Seminario Dottorato del Dipartimento di Matematica di Padova

Organization: Corrado Marastoni - Tiziano Vargiolu