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arXiv · 2008.11467

Frobenius functors and Gorenstein homological properties

Xiao-Wu Chen·Wei Ren
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Abstract

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.

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BibTeXRIS

Xiao-Wu Chen, Wei Ren. 2020-08-26. Frobenius functors and Gorenstein homological properties. https://doi.org/10.1016/j.jalgebra.2022.06.030

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