Balance of complete cohomology in extriangulated categories

Abstract

Let (C, E, s) be an extriangulated category with a proper class ξ of E-triangles. In this paper, we study the balance of complete cohomology in (C, E, s), which is motivated by a result of Nucinkis that complete cohomology of modules is not balanced in the way the absolute cohomology Ext is balanced. As an application, we give some criteria for identifying a triangulated catgory to be Gorenstein and an Artin algebra to be F -Gorenstein.