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 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 exploit the equivalence between t-structures and normal torsion theories on a stable
∞∞-category to show how a few classical topics in the theory of triangulated categories, ie …

Co-t-structures were introduced about ten years ago as a type of mirror image of t-structures.
Like t-structures, they permit us to divide an object in a triangulated category T into a “left …

We ask when a finite set of t-structures in a triangulated category can be 'averaged'into one t-
structure or, equivalently, when the extension closure of a finite set of aisles is again an …

We show that if a (not necessarily algebraic) triangulated category T contains an admissible
hereditary abelian subcategory H, then we can lift the inclusion of H into T to a fully faithful …

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 …

We define triangulated factorization systems on triangulated categories, and prove that a
suitable subclass thereof (the normal triangulated torsion theories) corresponds bijectively to …

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 …