On Rings and Functors: Pictures at an Exhibition

Abstract: It is banal to say that rings reveal their nature through their module categories. However, in the last few years we have seen indications that a similar statement can be made about stable module categories. Those are categories whose objects are the usual modules, but morphisms are formed by modding out maps factoring through projectives (or injectives). Additive functors defined on such categories are also said to be stable, and the study of such functors adds even more insights. The goal of this talk is to illustrate this thesis with simple examples. We shall see how several familiar classes of rings can be characterized by properties of their stable functors. This will be an expository talk. No prior knowledge of functor categories is assumed or needed.

rings and algebrasrepresentation theory

Audience: researchers in the topic

ONCAS Online Noncommutative Algebra Seminar

Series comments: This is an online seminar organized to keep the community of noncommutative algebraists connected during the pandemic which has made it difficult for everyone to travel. If you would like to attend these talks, please email to any of the organizers and you will be added to the mailing list.