论文标题
Frobenius Foundors和Gorenstein同源性能
Frobenius functors and Gorenstein homological properties
论文作者
论文摘要
我们证明，阿伯利亚类别之间的任何忠实的Frobenius函子都保留了物体的Gorenstein投影维度。因此，它保留并反映了戈伦斯坦的投影对象。我们提供条件，何时Frobenius Foundor分别保留了Gorenstein投射对象的稳定类别，奇异性类别和Gorenstein缺陷类别。在附录中，我们直接证明了以下已知结果：对于带有足够的投影和注射剂的Abelian类别，其全球Gorenstein投射维度与其全球Gorenstein Injexinive Vismension相吻合。
We prove that any faithful Frobenius functor between abelian categories preserves the Gorenstein projective dimension of objects. Consequently, it preserves and reflects Gorenstein projective objects. We give conditions on when a Frobenius functor preserves the stable categories of Gorenstein projective objects, the singularity categories and the Gorenstein defect categories, respectively. In the appendix, we give a direct proof of the following known result: for an abelian category with enough projectives and injectives, its global Gorenstein projective dimension coincides with its global Gorenstein injective dimension.
