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 describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

We describe a general correspondence between injective (resp. projective) recollements of
triangulated categories and injective (resp. projective) cotorsion pairs. This provides a model …

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 …

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 …

We study the behaviour of modules M that fit into a short exact sequence 0→ M→ C→ M→ 0,
where C belongs to a class of modules CC, the so-called C C-periodic modules. We find a …

Let R by a right coherent ring and R-Mod denote the category of left R-modules. We show
that there is an abelian model structure on R-Mod whose cofibrant objects are precisely the …

Let R be a commutative noetherian ring. We give criteria for a complex of cotorsion flat R-
modules to be minimal, in the sense that every self homotopy equivalence is an …

We develop in this paper the stable theory for projective complexes, by which we mean to
consider a chain complex of finitely generated projective modules as an object of the factor …

K-flatness for unbounded complexes of modules over a ring R was introduced by
Spaltenstein [27], as an analogue of the classical notion of flatness for modules. In this …