From sets to quivers: oidification and the Yang-Baxter equation

Abstract: The Yang-Baxter equation, or braid relation, can be defined in any monoidal category. In the category Set, much is known about its solutions. In this seminar I describe the monoidal category Quiv_\Lambda of quivers over a fixed set of vertices \Lambda. I introduce the philosophy called "oidification", which turns sets into quivers, groups into groupoids, algebras into algebroids, etc. Finally, I give an overview of the theory of the Yang-Baxter equation in Quiv_\Lambda, why it is relevant, what still works as in Set (and what works better than in Set!), and how it relates to the theory of partial solutions and partial algebraic structures.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar