Proper resolutions and Gorensteinness in extriangulated categories

doi:10.1007/s11464-021-0887-8

Frontiers of Mathematics in China

2021, Vol. 16

Issue (1): 95-117 https://doi.org/10.1007/s11464-021-0887-8

本期目录

Proper resolutions and Gorensteinness in extriangulated categories

Jiangsheng HU¹, Dondong ZHANG²(

), Panyue ZHOU³

¹. Department of Mathematics, Jiangsu University of Technology, Changzhou 213001, China
². Department of Mathematics, Zhejiang Normal University, Jinhua 321004, China
³. College of Mathematics, Hunan Institute of Science and Technology, Yueyang 414006, China

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Abstract：

Let $(ℓ, E, s)$ be an extriangulated category with a proper class $ξ$ of $E$ -triangles, and $W$ an additive full subcategory of $(ℓ, E, s)$ . We provide a method for constructing a proper $W ξ$ -resolution (resp., coproper $W ξ$ - coresolution) of one term in an $E$ -triangle in $ξ$ from that of the other two terms. By using this way, we establish the stability of the Gorenstein category $G W ξ$ in extriangulated categories. These results generalize the work of Z. Y. Huang [J. Algebra, 2013, 393: 142{169] and X. Y. Yang and Z. C. Wang [Rocky Mountain J. Math., 2017, 47: 1013{1053], but the proof is not too far from their case. Finally, we give some applications about our main results.

Key words： Proper resolution coproper coresolution extriangulated categories Gorenstein categories

收稿日期: 2020-01-20 出版日期: 2021-03-26

Corresponding Author(s): Dondong ZHANG

引用本文:

. [J]. Frontiers of Mathematics in China, 2021, 16(1): 95-117.
Jiangsheng HU, Dondong ZHANG, Panyue ZHOU. Proper resolutions and Gorensteinness in extriangulated categories. Front. Math. China, 2021, 16(1): 95-117.

链接本文:

https://academic.hep.com.cn/fmc/CN/10.1007/s11464-021-0887-8
https://academic.hep.com.cn/fmc/CN/Y2021/V16/I1/95

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