Proper classes and Gorensteinness in extriangulated categories
Proper classes and Gorensteinness in extriangulated categories
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DOI：
10.1016/j.jalgebra.2019.12.028
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发表时间：
2019-06
影响因子：
0.9
通讯作者：
Jiangsheng Hu;Dongdong Zhang;Panyue Zhou
中科院分区：
文献类型：
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作者：
Jiangsheng Hu;Dongdong Zhang;Panyue Zhou
外三角范畴由 Nakaoka 和 Palu 引入，作为精确范畴和三角范畴的同时概括。本文定义了外三角范畴中真类的概念。设C 是一个外三角范畴， Ψ 是C 中的一个真类。我们证明C 承认一个新的外三角结构。这种构造给出了外三角类别，它既不是精确类别，也不是三角类别。此外，我们在 C 语言中介绍和研究了 Ψ-Gorenstein 射影对象，并证明 Ψ-Gorenstein 射影对象与模块范畴或三角范畴中的 Gorenstein 射影对象共享一些基本属性。特别是，我们改进了 Asadollahi 和 Salarian (2004)[1] 的结果。作为应用，获得了外三角类别上可接受的模型结构。
Extriangulated categories were introduced by Nakaoka and Palu as a simultaneous generalization of exact categories and triangulated categories. A notion of proper class in an extriangulated category is defined in this paper. Let C be an extriangulated category and ξ a proper class in C. We prove that C admits a new extriangulated structure. This construction gives extriangulated categories which are neither exact categories nor triangulated categories. Moreover, we introduce and study ξ-Gorenstein projective objects in C and demonstrate that ξ-Gorenstein projective objects share some basic properties with Gorenstein projective objects in module categories or in triangulated categories. In particular, we refine a result of Asadollahi and Salarian (2004)[1]. As an application, the admissible model structure on extriangulated categories is obtained.