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 …

We define model structures on exact categories, which we call exact model structures. We
look at the relationship between these model structures and cotorsion pairs on the exact …

In this article we construct various models for singularity categories of modules over
differential graded rings. The main technique is the connection between abelian model …

We put a monoidal model category structure on the category of chain complexes of quasi-
coherent sheaves over a quasi-compact and semi-separated scheme X. The approach …

The unbounded derived category of a Grothendieck abelian category is the homotopy
category of a Quillen model structure on the category of unbounded chain complexes, where …

In this paper we develop the theory of operads, algebras and modules in cofibrantly
generated symmetric monoidal model categories. We give J-semi model strucures, which …

Our aim is to give a fairly complete account on the construction of compatible model
structures on exact categories and symmetric monoidal exact categories, in some cases …

Let $ C $ be an abelian category. We show that under certain hypotheses, a cotorsion pair
$(A, B) $ in $ C $ may induce two natural homological model structures on $ Ch (C) $. One …

Given a cotorsion pair $(\mathcal {A},\mathcal {B}) $ in an abelian category $\mathcal {C} $
with enough $\mathcal {A} $ objects and enough $\mathcal {B} $ objects, we define two …

There are many ways to present model categories, each with a different point of view. Here
we'd like to treat model categories as a way to build and control resolutions. This an …