A quasi-abelian category is an additive category with all kernels and cokernels, along with some additional conditions allowing us to extend notions from homological algebra to them. A key example is the category of complete bornological spaces which is derived equivalent to the category of inductive limits of Banach spaces. In this talk, we will introduce the key concepts in the theory of quasi-abelian categories and we will discuss their potential applications. In particular, we will see how we can extend ideas from Koszul duality to quasi-abelian categories, as well as their use more generally as a setting for a new theory of derived analytic geometry proposed by my supervisor Kobi Kremnizer and his collaborators.
This video is part of the New Directions in Group Theory and Triangulated Categories seminar series.
