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 generalize the small object argument in order to allow for its application to proper
classes of maps (as opposed to sets of maps in Quillen's small object argument). The …

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 …

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 $\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 …

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 …

For a small category AA, we prove that the homotopy colimit functor from the category of
simplicial diagrams on AA to the category of simplicial sets over the nerve of AA establishes …

We give a simultaneous generalization of exact categories and triangulated categories,
which is suitable for considering cotorsion pairs, and which we call extriangulated …

A Quillen model structure is presented by an interacting pair of weak factorization systems.
We prove that in the world of locally presentable categories, any weak factorization system …

We show that the abelian category mod-X of coherent functors over a contravariantly finite
rigid subcategory X in a triangulated category T is equivalent to the Gabriel–Zisman …