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 prove that given a Grothendieck category G with a tilting object of finite projective
dimension, the induced triangle equivalence sends an injective cogenerator of G to a big …

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 …

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 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 …

Every cotilting module over a ring R induces a t-structure with a Grothendieck heart in the
derived category D (Mod-R). We determine the simple objects in this heart and their injective …

Let G be a locally coherent Grothendieck category. We show that, under particular
conditions, if a t-structure τ in the unbounded derived category D (G) restricts to the bounded …

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 the notions of n-hereditary rings and its connection to the classes of finitely n-
presented modules, FP n-injective modules, FP n-flat modules and n-coherent rings. We …

We give a general construction of realization functors for $ t $-structures on the base of a
strong stable derivator. In particular, given such a derivator $\mathbb D $, a $ t $-structure …