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 …

Let R be a commutative ring. We show that any complete duality pair gives rise to a theory of
relative homological algebra, analogous to Gorenstein homological algebra. Indeed …

For a semiseparated noetherian scheme, we show that the category of cotorsion Gorenstein
flat quasi-coherent sheaves is Frobenius and a natural non-affine analogue of the category …

Let $ A $, $ B $ be two rings and $ T=\left (\begin {smallmatrix} A & M 0 & B\end
{smallmatrix}\right) $ with $ M $ an $ A $-$ B $-bimodule. Given two complete hereditary …

Let X be a class of left R-modules, Y be a class of right R-modules. In this article, we
introduce and study Gorenstein (X, Y)-flat modules as a common generalization of some …

Given two complete hereditary cotorsion pairs (Q, R) and (Q′, R′) in a bicomplete abelian
category G such that Q′⊆ Q and Q∩ R= Q′∩ R′, Becker showed that there exists a …