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 …

For any ring R we construct two triangulated categories, each admitting a functor from R-
modules that sends projective and injective modules to 0. When R is a quasi-Frobenius or …

Given a locally coherent Grothendieck category G, we prove that the homotopy category of
complexes of injective objects (also known as the coderived category of G) is compactly …

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 define the triangulated category of relative singularities of a closed subscheme in a
scheme. When the closed subscheme is a Cartier divisor, we consider matrix factorizations …

This is an overview on derived nonhomogeneous Koszul duality over a field, mostly based
on the author's memoir L. Positselski, Memoirs of the American Math. Society 212 (2011) …

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 …

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 …

Gorenstein homological algebra is a kind of relative homological algebra which has been
developed to a high level since more than four decades. In this report we review the basic …

Let $\kappa $ be a regular cardinal, $\lambda<\kappa $ be a smaller infinite cardinal, and
$\mathsf K $ be a $\kappa $-accessible category where colimits of $\lambda $-indexed …