Arkiv för Matematik
Volume 57 (2019)
Gorenstein flat precovers and Gorenstein injective preenvelopes in Grothendieck categories
Pages: 55 – 83
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
2010 Mathematics Subject Classification
Received 17 January 2017
Received revised 2 March 2018
Accepted 4 July 2018
Published 3 May 2019