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 is such that the …

The purpose of this paper is to describe a connection between model categories, a structure
invented by algebraic topologists that allows one to introduce the ideas of homotopy theory …

We show that if the given cotorsion pair in the category of modules is complete and
hereditary, then both of the induced cotorsion pairs in the category of complexes are …

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 …

An important example of a model category is the category of unbounded chain complexes of
R-modules, which has as its homotopy category the derived category of the ring R. This …

In [8] Sake introduced the notion of a cotorsion pair (A, B) in the category of abelian groups.
But his definitions and basic results carry over to more general abelian categories and have …

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 …

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 …

Let $\mathcal {A} $ be an abelian category, or more generally a weakly idempotent complete
exact category, and suppose we have two complete hereditary cotorsion pairs $(\mathcal …

Let $\mathbf {Ch}(\mathcal {O}) $ be the category of chain complexes of $\mathcal {O} $-
modules on a topological space $ T $(where $\mathcal {O} $ is a sheaf of rings on $ T $). We …