### Electronic Research Archive

2021, Issue 5: 3341-3359. doi: 10.3934/era.2021042

# Balance of complete cohomology in extriangulated categories

• Received: 01 September 2020 Revised: 01 May 2021 Published: 24 June 2021
• Primary: 16E30, 18G25; Secondary: 18G10

• 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.

Citation: Jiangsheng Hu, Dongdong Zhang, Tiwei Zhao, Panyue Zhou. Balance of complete cohomology in extriangulated categories[J]. Electronic Research Archive, 2021, 29(5): 3341-3359. doi: 10.3934/era.2021042

### Related Papers:

• 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.

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