We show that the category of orbits of the bounded derived category of a hereditary category
under a well-behaved autoequivalence is canonically triangulated. This answers a question …

We show that a certain orbit category considered by Keller encodes the combinatorics of the
m-clusters of Fomin and Reading in a fashion similar to the way the cluster category of Buan …

We prove a structure theorem for triangulated Calabi–Yau categories: an algebraic 2-Calabi–
Yau triangulated category over an algebraically closed field is a cluster category if and only …

The notion of an extriangulated category gives a unification of existing theories in exact or
abelian categories and in triangulated categories. In this article, we develop Auslander …

We introduce a new class of algebras, which we call cluster-tilted. They are by definition the
endomorphism algebras of tilting objects in a cluster category. We show that their …

Happel [6] and Cline, Parshall and Scott [4] showed that the tilting functors of Happel and
Ringel [8] can be interpreted in terms of an equivalence of derived categories of the module …

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 study (not necessarily connected) Z-graded A-infinity-algebras and their A-infinity-
modules. Using the cobar and the bar construction and Quillen's homotopical algebra, we …

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 introduce a new category C, which we call the cluster category, obtained as a quotient of
the bounded derived category D of the module category of a finite-dimensional hereditary …