Avramov-Martsinkovsky type exact sequences for extriangulated categories

Abstract

Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles. In this paper, we first introduce the ξ-Gorenstein cohomology in terms of ξ-Gprojective resolutions and ξ-Ginjective coresolutions, respectively, and then we get the balance of ξ-Gorenstein cohomology. Moreover, we study the interplay among ξ-cohomology, ξ-Gorenstein cohomology and ξ-complete cohomology, and obtain the Avramov-Martsinkovsky type exact sequences in this setting.