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 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 …

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 study the behavior of direct limits in the heart of a t-structure. We prove that, for any
compactly generated t-structure in a triangulated category with coproducts, countable direct …

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 …

Let G be a Grothendieck category, let t=(T, F) be a torsion pair in G and let (U t, W t) be the
associated Happel–Reiten–Smalø t-structure in the derived category D (G). We prove that …

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 …

In the setting of compactly generated triangulated categories, we show that the heart of a
(co) silting t-structure is a Grothendieck category if and only if the (co) silting object satisfies …

We study ideal cotorsion pairs associated to almost exact structures in extension closed
subcategories of triangulated categories. This approach allows us to extend the recent ideal …

It was shown recently that the heart H¯ of a twin cotorsion pair ((S, T),(U, V)) on an
extriangulated category is semi-abelian. We provide a sufficient condition for the heart to be …