论文标题
适当的分辨率和外侧类别中的戈伦斯坦内斯
Proper resolutions and Gorensteinness in extriangulated categories
论文作者
论文摘要
令$（\ Mathcal {C}，\ Mathbb {e}，\ Mathfrak {s}）$为外部类别，具有适当的类$之一的$ \ Mathbb {e} $ - triangles，$ \ Mathcal {w} $添加$ \ mathcal c $ \ mathcal c $。我们提供了一种方法来构建一个合适的$ \ MATHCAL {W}（ξ）$ - 分辨率（分别是coproper $ \ Mathcal {w}（W}（ξ）$ - coresolution）在$ \ Mathbb {e} $ - 三角形中的一个术语中的一个术语中的一个术语。通过以这种方式，我们在外节式类别中建立了Gorenstein类别$ \ Mathcal {GW}（ξ）$的稳定性。这些结果通过黄和杨华概括了他们的工作，但是证据与他们的案件不远。最后，我们提供了一些有关我们的主要结果的应用程序。
Let $(\mathcal{C},\mathbb{E},\mathfrak{s})$ be an extriangulated category with a proper class $ξ$ of $\mathbb{E}$-triangles, and $\mathcal{W}$ an additive full subcategory of $\mathcal C$. We provide a method for constructing a proper $\mathcal{W}(ξ)$-resolution (respectively, coproper $\mathcal{W}(ξ)$-coresolution) of one term in an $\mathbb{E}$-triangle in $ξ$ from that of the other two terms. By using this way, we establish the stability of the Gorenstein category $\mathcal{GW}(ξ)$ 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.
