## Geometry & Representation - Alistair Savage (University of Ottawa)

### Monday, January 7th, 2019

**Time:** 4:30-5:30 p.m. **Place:** Jeffery Hall 319

**Speaker:** Alistair Savage (University of Ottawa)

**Title:** Universal categories

**Abstract: ** Universal constructions are ubiquitous in mathematics. For example, the polynomial ring is uniquely characterized by a universal property for commutative rings. Other examples include free monoids, free groups, and tensor algebras. In this mainly expository talk we will discuss an analogous, but somewhat less well known, concept on the level of categories. In particular, we will see how one can define categories that are determined by universal properties. Examples include the Temperley--Lieb category (the free monoidal category on a self-dual object), the Brauer category (the free symmetric monoidal category on a self-dual object), and the oriented Brauer category (the free symmetric monoidal category on a pair of dual objects). We will discuss intuitive diagrammatic descriptions of these categories and how these universal constructions allow one to easily find deep symmetries in a wide range of categories.