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 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 …

The paper gives a new proof that the model categories of stable modules for the rings ℤ∕ p
2 and ℤ∕ p [ϵ]∕(ϵ 2) are not Quillen equivalent. The proof uses homotopy endomorphism …

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 …

We show that Quillenʼs small object argument works for exact categories under very mild
conditions. This has immediate applications to cotorsion pairs and their relation to the …

We construct Quillen equivalences between the model categories of monoids (rings),
modules and algebras over two Quillen equivalent model categories under certain …

The Grothendieck construction is a classical correspondence between diagrams of
categories and coCartesian fibrations over the indexing category. In this paper we consider …

We prove that given a Grothendieck category G with a tilting object of finite projective
dimension, the induced triangle equivalence sends an injective cogenerator of G to a big …

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 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 …