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Tilting subcategories with respect to cotorsion triples in abelian categories
- Part of
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- Journal:
- Proceedings of the Royal Society of Edinburgh. Section A: Mathematics / Volume 147 / Issue 4 / August 2017
- Published online by Cambridge University Press:
- 28 June 2017, pp. 703-726
- Print publication:
- August 2017
-
- Article
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Given a non-negative integer n and a complete hereditary cotorsion triple
, the notion of 
subcategories in an abelian category 
is introduced. It is proved that a virtually Gorenstein ring R is n-Gorenstein if and only if the subcategory 
of Gorenstein injective R-modules is 
with respect to the cotorsion triple 
, where 
stands for the subcategory of Gorenstein projectives. In the case when a subcategory 
of is closed under direct summands such that each object in 
admits a right -approximation, a Bazzoni characterization is given for to be . Finally, an Auslander–Reiten correspondence is established between the class of subcategories and that of certain subcategories of which are 
-coresolving covariantly finite and closed under direct summands.
, the notion of 
subcategories in an abelian category 
is introduced. It is proved that a virtually Gorenstein ring 
of Gorenstein injective 
with respect to the cotorsion triple 
, where 
stands for the subcategory of Gorenstein projectives. In the case when a subcategory 
of 
admits a right 
-coresolving covariantly finite and closed under direct summands.