We introduce a general version of the singular compactness theorem which makes it
possible to show that being a Σ Σ-cotorsion module is a property of the complete theory of …

Abstract We revisit Auslander–Buchweitz approximation theory and find some relations with
cotorsion pairs and model category structures. From the notion of relative generators, we …

A recent result by J. Šaroch and J. Šťovíček asserts that there is a unique abelian model
structure on the category of left R-modules, for any associative ring R with identity, whose …

We introduce a refinement of the Gorenstein flat dimension for complexes over an
associative ring—the Gorenstein flat-cotorsion dimension—and prove that it, unlike the …

We introduce a notion of total acyclicity associated to a subcategory of an abelian category
and consider the Gorenstein objects they define. These Gorenstein objects form a Frobenius …

We define the projective stable category of a coherent scheme. It is the homotopy category
of an abelian model structure on the category of unbounded chain complexes of quasi …

We systematically develop, study, and give applications of definable functors between
compactly generated triangulated categories. Such functors preserve pure triangles, pure …

A model structure on a category is a formal way of introducing a homotopy theory on that
category, and if the model structure is abelian and hereditary, its homotopy category is …

We study Gorenstein flat objects in the category Rep (Q, R) of representations of a left rooted
quiver Q with values in Mod (R), the category of all left R-modules, where R is an arbitrary …

We study approximations of modules of finite Gorenstein flat dimension by (projectively
coresolved) Gorenstein flat modules and modules of finite flat dimension. These …