In this paper we introduce a new notion of weight structure (w) for a triangulated category C;
this notion is an important natural counterpart of the notion of t-structure. It allows extending …

Derived equivalences and t-structures are closely related. We use realisation functors
associated to t-structures in triangulated categories to establish a derived Morita theory for …

We describe a new method for constructing a weight structure $ w $ on a triangulated
category $ C $. For a given $ C $ and $ w $ it allow us to give a fairly comprehensive (and …

The main goal of this paper is to define the Chow weight structure w Chow for the category
DM c (S) of (constructible) Beilinson motives over any excellent separated finite-dimensional …

We show that representations of convolution algebras such as Lustzig's graded affine Hecke
algebra or the quiver Hecke algebra and quiver Schur algebra in type A and A˜ can be …

This paper is dedicated to new methods of constructing weight structures and weight-exact
localizations; our arguments generalize their bounded versions considered in previous …

In the paper, we define the notion of a state BCK-algebra and a state-morphism BCK-
algebra extending the language of BCK-algebras by adding a unary operator which models …

We study a diagrammatic categorification (the" anti-spherical category") of the anti-spherical
module for any Coxeter group. We deduce that Deodhar's (sign) parabolic Kazhdan-Lusztig …

We present simple conditions which guarantee a geometric extension algebra to behave
like a variant of quasi-hereditary algebras. In particular, standard modules of affine Hecke …

Consider the obvious functor from the unbounded derived category of all finitely generated
modules over a left noetherian ring R to the unbounded derived category of all modules. We …