REPRESENTATION THEORY AND RELATED TOPICS SEMINAR

ABSTRACT: Quillen exact categories generalise the important and widely used notion of abelian categories. We discuss ways to generalise the intersections and sums of subobjects to the realm of exact categories. The first way, using pushouts and pullbacks, leads to new characterisations of quasi-abelian and abelian categories, and motivates the general way. We introduce general notions of intersection and sum that allows us to consider the Artin-Wedderburn exact categories and generalise the famous Jordan-Hölder theorem.

This talk is based on two joint works, one with T.Brüstle and A.Tattar and another one with A.Shah and S-A.Wegner.