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 …

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 …

Let $ R $ be a ring and Ch ($ R $) the category of chain complexes of $ R $-modules. We
put an abelian model structure on Ch ($ R $) whose homotopy category is equivalent to $ K …

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 …

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 …

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 …

Given a diagram of rings, one may consider the category of modules over them. We are
interested in the homotopy theory of categories of this type: given a suitable diagram of …

Let D be a category and E a class of morphisms in D. In this paper we study the question of
how to transfer homotopic structure from the category of simplicial objects in D, Δ∘ D, to D …

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 …

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 …