Let A be an artin algebra and modA the category of finitely generated A-modules. Unless
stated to the contrary, by a subcategory C of a category we mean a full subcategory of an …

The aim of this paper is to introduce τ-tilting theory, which 'completes'(classical) tilting theory
from the viewpoint of mutation. It is well known in tilting theory that an almost complete tilting …

In our previous article, we constructed an abelian category from any torsion pair on a
triangulated category. This generalizes the heart of a t-structure and the ideal quotient by a …

We study irreducible morphisms in the bounded derived category of finitely generated
modules over an Artin algebra Λ, denoted Db (Λmod), by means of the underlying category …

For any left R-module P with endomorphism ring S, the adjoint pair of functors P⊗ S− and
HomR (P,−) induce an equivalence between the categories of P-static R-modules and P …

A length category ce is an abelian category in which all objects have finite length. It is called
hereditary, provided Exe vanishes everywhere. Since a length category with only a set of …

In [R. Colpi, KR Fuller, Tilting objects in abelian categories and quasitilted rings, Trans.
Amer. Math. Soc., in press] tilting objects in an arbitrary abelian category H are introduced …

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 …

We show that there is a one-to-one correspondence between basic cotilting complexes and
certain contravariantly finite subcategories of the bounded derived category of an artin …

We show that a tilting module T over a ring R admits an exact sequence 0→ R→ T 0→ T 1→
0 such that T_0,T_1∈Add(T) and Hom R (T 1, T 0)= 0 if and only if T has the form S⊕ S/R for …