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arXiv · 2001.11352

Proper resolutions and Gorensteinness in extriangulated categories

Jiangsheng Hu·Dongdong Zhang·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, and $\mathcal{W}$ an additive full subcategory of $\mathcal C$. We provide a method for constructing a proper $\mathcal{W}(\xi)$-resolution (respectively, coproper $\mathcal{W}(\xi)$-coresolution) of one term in an $\mathbb{E}$-triangle in $\xi$ from that of the other two terms. By using this way, we establish the stability of the Gorenstein category $\mathcal{GW}(\xi)$ in extriangulated categories. These results generalise their work by Huang and Yang-Wang, but the proof is not too far from their case. Finally, we give some applications about our main results.

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Jiangsheng Hu, Dongdong Zhang, Panyue Zhou. 2020-01-29. Proper resolutions and Gorensteinness in extriangulated categories. https://arxiv.org/abs/2001.11352

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