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 …

We introduce the notion of noncompact (partial) silting and (partial) tilting sets and objects in
any triangulated category D with arbitrary (set-indexed) coproducts. We show that …

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 …

Recent results by Keller and Nicolás and by Koenig and Yang have shown bijective
correspondences between suitable classes of t-structures and cot-structures with certain …

Suppose that $\mathcal {A} $ is an abelian category whose derived category $\mathcal
{D}(\mathcal {A}) $ has $ Hom $ sets and arbitrary (small) coproducts, let $ T $ be a (not …

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 …

We introduce and develop an analogous of the Auslander–Buchweitz approximation theory
(see Auslander and Buchweitz, Societe Mathematique de France 38: 5–37, 1989) in the …

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 …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

We define the notion of cobordism of two objects in a triangulated category, and the Witt
group of such category is defined as the Grothendieck group of cobordism classes of self …