On the classification of silting subcategories in the stable category of Frobenius extriangulated categories
On the classification of silting subcategories in the stable category of Frobenius extriangulated categories
复制标题
DOI：
--
复制
发表时间：
2020-12
期刊：
影响因子：
--
通讯作者：
Yajun Ma;Nanqing Ding;Yafeng Zhang;Jiangsheng Hu
中科院分区：
文献类型：
--
作者：
Yajun Ma;Nanqing Ding;Yafeng Zhang;Jiangsheng Hu
我们将所有淤积子类别分类为 Frobenius 外三角类别的稳定类别，概括了 Di 等人的结果。 (J. Algebra 525 (2019) 42-63) 关于三角类别上淤积子类别的 Auslander-Reiten 类型对应。更具体地说，对于任何 Frobenius 外三角范畴 $\mathcal{C}$，我们在稳定范畴 $\underline{\mathcal{C}}$ 的淤积子类别和 $\mathcal{C}$ 的某些协变有限子类别之间建立双射对应关系。因此，Frobenius 精确类别的稳定类别中的所有淤积子类别均被分类。该结果应用于具有足够射影的阿贝尔范畴上的同伦范畴、具有足够射影的格罗腾迪克范畴上的派生范畴以及环 $R$ 上的 Gorenstein 射影模的稳定范畴。
We classify all silting subcategories in the stable category of Frobenius extriangulated categories, generalizing the result of Di et al. (J. Algebra 525 (2019) 42-63) about the Auslander-Reiten type correspondence for silting subcategories over triangulated categories. More specifically, for any Frobenius extriangulated category $\mathcal{C}$, we establish the bijective correspondence between silting subcategories of the stable category $\underline{\mathcal{C}}$ and certain covariantly finite subcategories of $\mathcal{C}$. As a consequence, all silting subcategories in the stable category of Frobenius exact categories are classified. This result is applied to homotopy categories over abelian categories with enough projectives, derived categories over Grothendieck categories with enough projectives as well as to the stable category of Gorenstein projective modules over a ring $R$.