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) …

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 …

Contraherent cosheaves are globalizations of cotorsion (or similar) modules over
commutative rings obtained by gluing together over a scheme. The category of contraherent …

We prove general results about completeness of cotorsion theories and existence of covers
and envelopes in locally presentable abelian categories, extending the well-established …

This monograph provides an overview on the Maurer-Cartan methods in algebra, geometry,
topology, and mathematical physics. It offers a conceptual, exhaustive and gentle treatment …

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 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 …

We show that there is an equivalence of $\infty $-categories between Lie algebroids and
certain kinds of curved Lie algebras. For this we develop a method to study the $\infty …

Orlov's famous representability theorem asserts that any fully faithful exact functor between
the bounded derived categories of coherent sheaves on smooth projective varieties is a …