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Frobenius functors and Gorenstein homological properties | Xiao-Wu Chen
; Wei Ren
; | Date: |
26 Aug 2020 | 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. | Source: | arXiv, 2008.11467 | Services: | Forum | Review | PDF | Favorites |
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