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Gorenstein flat precovers and Gorenstein injective preenvelopes in Grothendieck categories

Edgar Enochs University of Kentucky J.R. García Rozas University of Almería Luis Oyonarte University of Almería Blas Torrecillas University of Almería

Category Theory mathscidoc:1912.43029

Arkiv for Matematik, 57, (1), 55-83, 2019
Homology theory relative to classes of objects other than those of projective or injective objects in abelian categories has been widely studied in the last years, giving a special relevance to Gorenstein homological algebra. We prove the existence of Gorenstein flat precovers in any locally finitely presented Grothendieck category in which the class of flat objects is closed under extensions, the existence of Gorenstein injective preenvelopes in any locally noetherian Grothendieck category in which the class of all Gorenstein injective objects is closed under direct products, and the existence of special Gorenstein injective preenvelopes in locally noetherian Grothendieck categories with a generator lying in the left orthogonal class to that of Gorenstein injective objects.
Gorenstein flat object, Gorenstein injective object, Grothendieck category, precover, preenvelope
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@inproceedings{edgar2019gorenstein,
  title={Gorenstein flat precovers and Gorenstein injective preenvelopes in Grothendieck categories},
  author={Edgar Enochs, J.R. García Rozas, Luis Oyonarte, and Blas Torrecillas},
  url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204133005024754585},
  booktitle={Arkiv for Matematik},
  volume={57},
  number={1},
  pages={55-83},
  year={2019},
}
Edgar Enochs, J.R. García Rozas, Luis Oyonarte, and Blas Torrecillas. Gorenstein flat precovers and Gorenstein injective preenvelopes in Grothendieck categories. 2019. Vol. 57. In Arkiv for Matematik. pp.55-83. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20191204133005024754585.
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