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 …

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 …

Tilting theory has been a very important tool in the classification of finite dimensional
algebras of finite and tame representation type, as well as, in many other branches of …

We show that a right triangulated category is best behaved when its shift satisfies conditions
making it what we call a right semi-equivalence. We consider right triangulated categories …

Tilting modules appear in a variety of ways: their first definition was in the context of finite
dimensional algebras over a field. Later, they appeared naturally in applications of the …

Tilting modules arose from representation theory of algebras and are known to furnish
equivalences between categories of modules. We single out some weaker properties which …

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 …

Motivated by its links to τ-tilting theory, we introduce left weak cotorsion pairs, as a
generalization of cotorsion pairs in module categories. Such pairs are also linked to co-t …

In a compactly generated triangulated category, we introduce a class of tilting objects
satisfying a certain purity condition. We call these the decent tilting objects and show that the …