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 …

Given small dg categories A and B and a BA-bimodule T, we give necessary and sufficient
conditions for the associated derived functors of Hom and the tensor product to be fully …

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 …

We define the notion of an infinitely generated tilting object of infinite homological dimension
in an abelian category. A one-to-one correspondence between∞-tilting objects in complete …

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 …

In this paper we introduce a special kind of relative (co) resolutions associated to a pair of
classes of objects in an abelian category $\mathcal {C}. $ We will see that, by studying these …

Let $\mathcal {A} $ be a Hom-finite abelian category with enough projectives. In this note,
we show that any covariantly finite $\tau $-rigid subcategory is contained in a support $\tau …

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 define tilting subcategories in arbitrary exact categories to archieve the following. Firstly:
Unify existing definitions of tilting subcategories to arbitrary exact categories. Discuss …

The aim of this paper is to develop a framework for localization theory of triangulated
categories\(\mathcal {C}\), that is, from a given extension-closed subcategory\(\mathcal {N}\) …