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 …

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 …

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 …

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 …

We explore the interplay between t‐structures in the bounded derived category of finitely
presented modules and the unbounded derived category of all modules over a coherent ring …

Let be a triangulated category with shift functor. Suppose is a co-t-structure with coheart and
extended coheart, which is an extriangulated category. We show that there is a bijection …

Silting modules are abundant. Indeed, they parametrise the definable torsion classes over a
noetherian ring, and the hereditary torsion pairs of finite type over a commutative ring. Also …