To a big-tilting object in a complete, cocomplete abelian category with an injective
cogenerator we assign a big-cotilting object in a complete, cocomplete abelian category with …

We show that every flat quasi-coherent sheaf on a quasi-compact quasi-separated scheme
is a directed colimit of locally countably presentable flat quasi-coherent sheaves. More …

The concept of an abelian DG-category, introduced by the first-named author in arXiv:
2110.08237, unites the notions of abelian categories and (curved) DG-modules in a …

A locally coherent exact category is a finitely accessible additive category endowed with an
exact structure in which the admissible short exact sequences are the directed colimits of the …

The phenomenon of periodicity, discovered by Benson and Goodearl, is linked to the
behavior of the objects of cocycles in acyclic complexes. It is known that any flat Proj …

We define and study the derived categories of the first kind for curved DG and A-infinity
algebras complete over a pro-Artinian local ring with the curvature elements divisible by the …

Contramodules are module-like algebraic structures endowed with infinite summation (or,
occasionally, integration) operations satisfying natural axioms. Introduced originally by …

For a locally presentable abelian category B with a projective generator, we construct the
projective derived and contraderived model structures on the category of complexes …

We continue investigating the interaction between flatness and a a-adic completion for
infinitely generated A-modules. Here A is a commutative ring and aa is a finitely generated …

For four wide classes of topological rings R, we show that all flat left R-contramodules have
projective covers if and only if all flat left R-contramodules are projective if and only if all left …