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) …

We give an overview of recent developments in silting theory. After an introduction on torsion
pairs in triangulated categories, we discuss and compare different notions of silting and …

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 …

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

We study when the heart of at-structure in a triangulated category D with coproducts is AB5
or a Grothendieck category. If D satisfies Brown representability, at-structure has an AB5 …

This paper is a follow-up to arXiv: 2212.09639. We consider two algebraic settings of
comodules over a coring and contramodules over a topological ring with a countable base …

We develop theory of (possibly large) cotilting objects of injective dimension at most one in
general Grothendieck categories. We show that such cotilting objects are always pure …

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 …

We construct an" almost involution" assigning a new DG-category to a given one, and use
this construction in order to recover, say, the abelian category of graded modules over the …

In the derived category of a commutative noetherian ring, we explicitly construct a silting
object associated with each sp-filtration of the Zariski spectrum satisfying the “slice” …