From certain triangle functors, called nonnegative functors, between the bounded derived
categories of abelian categories with enough projective objects, we introduce their stable …

Abstract Let AA and BB be abelian categories and F: A → BF: A→ B an additive and right
exact functor which is perfect, and let (F, B)(F, B) be the left comma category. We give an …

An extension $ B\subset A $ of finite dimensional algebras is bounded if the $ B $-$ B $-
bimodule $ A/B $ is $ B $-tensor nilpotent, its projective dimension is finite and $\mathrm …

Let C be an abelian or exact category with enough projectives and let P be the full
subcategory of projective objects of C. We consider the stable category C/P modulo …

We investigate relative cohomology functors on subcategories of abelian categories via
Auslander-Buchweitz approximations and the resulting strict resolutions. We verify that …

For any ring R, we show that, in the bounded derived category Db (Mod R) of le R-modules,
the subcategory of complexes with nite Gorenstein projective (resp. injective) dimension …

Let A be an abelian category and C an additive full subcategory of A. We provide a method
to construct a proper C-resolution (resp. coproper C-coresolution) of one term in a short …

We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

We develop in this paper the stable theory for projective complexes, by which we mean to
consider a chain complex of finitely generated projective modules as an object of the factor …

We prove that any faithful Frobenius functor between abelian categories preserves the
Gorenstein projective dimension of objects. Consequently, it preserves and reflects …