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 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 …

In the preceding part (I) of this paper, we showed that for any torsion pair (ie, t-structure
without the shift-closedness) in a triangulated category, there is an associated abelian …

arXiv:0710.5065v3 [math.AT] 28 Oct 2008 Page 1 arXiv:0710.5065v3 [math.AT] 28 Oct 2008
ON DERIVED CATEGORIES AND DERIVED FUNCTORS SAMSON SANEBLIDZE Abstract …

Whereas formal category theory is classically considered within a $2 $-category, in this
paper a double-dimensional approach is taken. More precisely we develop such theory …

We show that the relative Auslander-Buchweitz context on a triangulated category $\T $
coincides with the notion of co-$ t $-structure on certain triangulated subcategory of $\T …

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 show that the relative Auslander–Buchweitz context on a triangulated category T
coincides with the notion of co-t-structure on certain triangulated subcategory of T (see …

The derived category D [C, V] of the Grothendieck category of enriched functors [C, V], where
V is a closed symmetric monoidal Grothendieck category and C is a small V-category, is …