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 …

Mutation of compact silting objects is a fundamental operation in the representation theory of
finite-dimensional algebras due to its connections to cluster theory and to the lattice of …

We study t-structures with Grothendieck hearts on compactly generated triangulated
categories TT that are underlying categories of strong and stable derivators. This setting …

The aim of this work is to construct certain homotopy t-structures on various categories of
motivic homotopy theory, extending works of Voevodsky, Morel, Déglise and Ayoub. We …

An important result in tilting theory states that a class of modules over a ring is a tilting class
if and only if it is the Ext-orthogonal class to a set of compact modules of bounded projective …

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 …

We give criteria for subcategories of a compactly generated algebraic triangulated category
to be precovering or preenveloping. These criteria are formulated in terms of closure …

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

This paper is dedicated to the study of smashing weight structures (these are the weight
structures" coherent with coproducts"), and the application of their properties to t-structures …

We prove that, given any strong and stable derivator and a t-structure in its base triangulated
category D, the t-structure canonically lifts to all the (coherent) diagram categories and each …