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arXiv · 2004.13711

Balance of complete cohomology in extriangulated categories

Jiangsheng Hu·Dongdong Zhang·Tiwei Zhao·Panyue Zhou
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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.

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Jiangsheng Hu, Dongdong Zhang, Tiwei Zhao, Panyue Zhou. 2020-04-28. Balance of complete cohomology in extriangulated categories. https://doi.org/10.3934/era.2021042

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