Sondre Kvamme (Bonn)

A generalization of finite-dimensional Iwanaga-Gorenstein algebra.

Abstract:

We study abelian categories equipped with a comonad and a Nakayama functor relative to the comonad. This generalizes properties of the module category of a finite-dimensional algebra from the viewpoint of Gorenstein homological algebra. In particular, we obtain a generalization of Zaks theorem on the equality of the left and right injective dimension of an Iwanaga-Gorenstein algebra. The theory can be applied to functor categories of abelian categories, and we use this to give a description of the Gorenstein projective objects in such categories.