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 …

We introduce the right (left) Gorenstein subcategory relative to an additive subcategory CC
of an abelian category AA, and prove that the right Gorenstein subcategory rG (G (C) G (C)) …

Let A be an abelian category. For a pair (X, Y) of classes of objects in A, we define the weak
and the (X, Y)-Gorenstein relative projective objects in A. We point out that such objects …

We revisit a construction of wide subcategories going back to work of Ingalls and Thomas.
To a torsion pair in the category $ R\operatorname {-}\operatorname {mod} $ of finitely …

We introduce symmetric subcategories of abelian categories and show that the derived
category of the endomorphism ring of any good tilting module over a ring is a recollement of …

We study homological behavior of modules satisfying the Auslander condition. Assume that
AC is the class of left R-modules satisfying the Auslander condition. It is proved that each …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

We define the symmetric Auslander category As (R) to consist of complexes of projective
modules whose left-and right-tails are equal to the left-and right-tails of totally acyclic …

Motivated by some properties satisfied by Gorenstein projective and Gorenstein injective
modules over an Iwanaga-Gorenstein ring, we present the concept of left and right n …

We introduce the notion of balanced pair of additive subcategories in an abelian category.
We give sufficient conditions under which a balanced pair of subcategories gives rise to a …