ABSTRACT A natural generalization of locally noetherian and locally coherent categories
leads us to define locally type FP∞ categories. They include not just all categories of …

For any ring R we construct two triangulated categories, each admitting a functor from R-
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or …

Let R be any ring with identity and Ch (R) C h (R) the category of chain complexes of (left) R-
modules. We show that the Gorenstein AC-projective chain complexes of 1 are the cofibrant …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type $\text {FP} _n $ and studying their closure properties with respect to short …

Consider the obvious functor from the unbounded derived category of all finitely generated
modules over a left noetherian ring R to the unbounded derived category of all modules. We …

We study finiteness conditions in Grothendieck categories by introducing the concepts of
objects of type FP n and studying their closure properties with respect to short exact …

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 …

Absolutely clean and level R-modules were introduced in and used to show how Gorenstein
homological algebra can be extended to an arbitrary ring R. This led to the notion of …

Mod ª Ex C, Ab, M¬ Hom y, M my Ž. Ž. Ž. is an equivalence. Thus we can replace a-module
by an exact functor Ž. op C ª Ab. Of course, since the work of Auslander, it has been common …

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