We study homotopy categories of model categories arising from a cotorsion triple, and the
equivalences between corresponding stable categories. We characterize homological …

A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …

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

First we study the Gorenstein cohomological dimension ${\rm Gcd} _RG $ of groups $ G $
over coefficient rings $ R $, under changes of groups and rings; a characterization for …

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

Let 𝒜 be an abelian category. A subcategory 𝒳 of 𝒜 is called coresolving if 𝒳 is closed under
extensions and cokernels of monomorphisms and contains all injective objects of 𝒜. In this …

Let $\mathcal {C} $ be a triangulated category with a proper class $\xi $ of triangles.
Asadollahi and Salarian introduced and studied $\xi $-Gorenstein projective and $\xi …

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 …

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 …

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 …