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 …

Let $ S $ and $ R $ be rings and $ _SC_R $ a (faithfully) semidualizing bimodule. We
introduce and study $ C $-weak flat and $ C $-weak injective modules as a generalization of …

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 …

Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …

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

Given a non-negative integer n and a ring R with identity, we construct a hereditary abelian
model structure on the category of left R-modules where the class of cofibrant objects …

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 …

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 …

We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …