Proper resolutions and Gorensteinness in extriangulated categories

Jiangsheng HU; Dondong ZHANG; Panyue ZHOU

doi:10.1007/s11464-021-0887-8

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Front. Math. China ›› 2021, Vol. 16 ›› Issue (1) : 95-117. DOI: 10.1007/s11464-021-0887-8

RESEARCH ARTICLE

Proper resolutions and Gorensteinness in extriangulated categories

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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.

Keywords

Proper resolution / coproper coresolution / extriangulated categories / Gorenstein categories

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Jiangsheng HU, Dondong ZHANG, Panyue ZHOU. Proper resolutions and Gorensteinness in extriangulated categories. Front. Math. China, 2021, 16(1): 95‒117 https://doi.org/10.1007/s11464-021-0887-8

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