Abstract We consider a Krull–Schmidt, Hom-finite, 2-Calabi–Yau triangulated category with
a basic rigid object T, and show a bijection between the set of isomorphism classes of basic …

The class of support-tilting modules was introduced recently by Adachi et al. These modules
complete the class of tilting modules from the point of view of mutations. Given a finite …

In this paper we continue the project of generalizing tilting theory to the category of
contravariant functors Mod(C), from a skeletally small preadditive category C to the category …

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 …

Building on the embedding of an n-abelian category into an abelian category as an n-cluster-
tilting subcategory of, in this paper, we relate the n-torsion classes of with the torsion classes …

The concept of*-module arose from a remarkable converse of the tilting theorem due to
Menini and Orsatti [25] who essentially proved that for suitable full subcategories G & R-Mod …

Let TR be a right n-tilting module over an arbitrary associative ring R. In this paper we prove
that there exists a n-tilting module T′ R equivalent to TR which induces a derived …

Let $\mathcal C $ be a Krull-Schmidt triangulated category with shift functor $[1] $ and
$\mathcal R $ be a rigid subcategory of $\mathcal C $. We are concerned with the mutation …

In an ongoing project to classify all hereditary abelian categories, we provide a classification
of $\operatorname {Ext} $-finite directed hereditary abelian categories satisfying Serre …

An abelian category with arbitrary coproducts and a small projective generator is equivalent
to a module category (Mitchell (1964)[17]). A tilting object in an abelian category is a natural …