Balance of complete cohomology in extriangulated categories

Abstract

Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $\xi$ of $\mathbb{E}$-triangles. In this paper, we study the balance of complete cohomology in $(\mathcal{C},\mathbb{E},\mathfrak{s})$, 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.

18 pages. arXiv admin note: text overlap with arXiv:2003.11852, arXiv:1908.00931

References in corpus (1)

• Complete cohomology for extriangulated categories

Cited by in corpus (2)

• Avramov-Martsinkovsky type exact sequences for extriangulated categories
• Gorenstein Objects in Extriangulated Categories