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) …

This paper surveys bocses, quasi-hereditary algebras and their relationship which was
established in a recent result by Koenig, Ovsienko, and the author. Particular emphasis is …

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

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

The purpose of this paper is to develop a theory of bimonads and Hopf monads on arbitrary
categories thus providing the possibility to transfer the essentials of the theory of Hopf …

We prove that the category of modules over a separable ring object in a tensor triangulated
category admits a unique structure of triangulated category which is compatible with the …

We relate two different proposals to extend the étale topology into homotopy theory, namely
via the notion of finite cover introduced by Mathew and via the notion of separable …

We introduce heavily separable functors of the second kind and study them in three different
situations. The first of these is with restrictions and extensions of scalars for modules over …

Let X be a K3 surface and M a smooth and projective moduli space of stable sheaves on X
of Mukai vector v. A universal sheaf U over X x M induces an integral transform F from the …

For an adjoint pair (F, U)(F, U) of functors, we prove that UU is a separable functor if and only
if the defined monad is separable and the associated comparison functor is an equivalence …