Calabi-Yau triangulated categories Page 483 Calabi-Yau triangulated categories Bernhard
Keller 1 Introduction These notes reflect the contents of three lectures given at the workshop …

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 …

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 …

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 …

We investigate cluster-tilting objects (and subcategories) in triangulated 2-Calabi–Yau and
related categories. In particular, we construct a new class of such categories related to …

We study Auslander correspondence from the viewpoint of higher-dimensional analogue of
Auslander–Reiten theory [O. Iyama, Higher dimensional Auslander–Reiten theory on …

For each positive integer n we introduce the notion of n-exangulated categories as higher
dimensional analogues of extriangulated categories defined by Nakaoka–Palu. We …

The concept of cluster tilting gives a higher analogue of classical Auslander correspondence
between representation-finite algebras and Auslander algebras. The n-Auslander–Reiten …

A general framework for cluster tilting is set up by showing that any quotient of a triangulated
category modulo a tilting subcategory (ie, a maximal 1-orthogonal subcategory) carries an …

We say that an algebra $\Lambda $ over a commutative noetherian ring $ R $ is Calabi-Yau
of dimension $ d $($ d $-CY) if the shift functor $[d] $ gives a Serre functor on the bounded …