Contravariantly finite resolving subcategories of the category of finitely generated modules
have been playing an important role in the representation theory of algebras. In this paper …

We prove the following results for the subcategories of an abelian category: 1) The full
subcategory whose objects are kernels of the maps between two covariantly finite …

Let A be a right coherent ring and X be a contravariantly finite subcategory of mod-A
containing projectives. In this paper, we construct a recollement of abelian categories (mod0 …

Let Mod-S denote the category of S-modules, where S is a small pre-additive category.
Using the notion of relative derived categories of functor categories, we generalize Rickard's …

Let R be a quotient ring of a commutative coherent regular ring by a finitely generated ideal.
Hovey gave a bijection between the set of coherent subcategories of the category of finitely …

The paper is devoted to study some of the questions arises naturally in connection to the
notion of relative derived categories. In particular, we study invariants of recollements …

Let XX be a resolving subcategory of an abelian category. In this paper we investigate the
singularity category D_ sg (X)= D^ b (mod\, X)/K^ b (proj (mod\, X)) D sg (X ̲)= D b (mod X …

Let R be a commutative Noetherian ring. Denote by mod R the category of finitely generated
R-modules. In this paper, we study dominant resolving subcategories of mod R. We …

Let R be a commutative Noetherian local ring with residue field k. Let X be a resolving
subcategory of finitely generated R-modules. This paper mainly studies when X contains k …

Let $ A $ be a commutative noetherian ring. In this paper, we interpret localizing
subcategories of the derived category of $ A $ by using subsets of Spec $ A $ and …