**An Introduction to Categories:****Why They Give Us New Insight**

Alex Levin

University of New Hampshire

Friday, April 26th, 4:30 PM

Kalkin 001

**Abstract**

We will introduce categories in a self-contained way and give some fundamental examples. Two principles that are ubiquitous in category theory are the notions of compatibility of structures and coherence of families of morphisms. Many definitions and constructions become much easier to read (or even to guess!) when approached with those principles in mind. As illustrations we will construct monoidal categories, which allow us to study generalized notions of associativity, and braided monoidal categories, which allow us to study generalized notions of commutativity. We will also discuss dividends of the categorical perspective, such as applications in classical algebra or computer science.

ADA: Individuals requiring accommodations, please contact Doreen Taylor at (802) 656-3166