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 …

In a paper from 2002, Hovey introduced the Gorenstein projective and Gorenstein injective
model structures on R-Mod, the category of R-modules, where R is any Gorenstein ring …

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 …

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

We consider the homotopy category of complexes of projective modules over a Noetherian
ring. Truncation at degree zero induces a fully faithful triangle functor from the totally acyclic …

We introduce the notion of relative singularity category with respect to a self‐orthogonal
subcategory ω of an abelian category. We introduce the Frobenius category of ω‐Cohen …

We make a general study of Quillen model structures on abelian categories. We show that
they are closely related to cotorsion pairs, which were introduced by Salce [Sal79] and have …

A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose …

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 …

We investigate the properties of categories of GC-flat R-modules where C is a semidualizing
module over a commutative noetherian ring R. We prove that the category of all GC-flat R …