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 …

This is the second revised edition of an introduction to contemporary relative homological
algebra. It supplies important material essential to understand topics in algebra, algebraic …

References Page 1 References [1] S. Abhyankar, S. Wiegand, On the compositum of two power
series rings, Proc. Amer. Math. Soc. 112 (1991), 629 – 636. [2] U. Albrecht, Endomorphism …

Mutation in triangulated categories and rigid Cohen–Macaulay modules Page 1 DOI:
10.1007/s00222-007-0096-4 Invent. math. 172, 117–168 (2008) Mutation in triangulated …

The class of support-tilting modules was introduced to provide a completion of the class of
tilting modules from the point of view of mutations. In this article, we study-tilting finite …

In this paper the authors investigate homological and homotopical aspects of a concept of
torsion which is general enough to cover torsion and cotorsion pairs in abelian categories …

zeltschrlft Page 1 Math. 2. 208, 2097223 (1991) Mathemattsche zeltschrlft © Springer-Veda g
1991 The category of modules with good filtrations over a quasi-hereditary algebra has almost …

In an additive category with direct limits, an object X is said to be finitely presented provided
that the representable functor Hom (X,-1 commutes with direct limits, and ignoring a set …

Modern developments in representation theory rely heavily on homological methods. This
book for advanced graduate students and researchers introduces these methods from their …

We prove that in a 2-Calabi–Yau triangulated category, each cluster tilting subcategory is
Gorenstein with all its finitely generated projectives of injective dimension at most one. We …