Representation Theory of Algebras: New results

BIREP: Representation Theory of Algebras: Striking New Results. (Compiled by C.M.Ringel)

Example Nr.2

A triangulated category which is not even topological

Muro: The category of free Z/4-modules can be made into a triangulated category with the identity functor as shift functor and such that the sequence Z/4 → Z/4 → Z/4 → Z/4 (with all maps being multiplication by 2) is a triangle.

This triangulated category is not algebraic, not even topological.

Definitions: A triangulated category is

algebraic iff it is a full triangulated subcategory of the stable category of a Frobenius category;
topological iff it is a full triangulated subcategory of the homotopy category of a stable model category.
Note: All algebraic triangulated categories are topological (the converse is not true).

Fakultät für Mathematik, Universität Bielefeld
Verantwortlich: C.M.Ringel
E-Mail: ringel@math.uni-bielefeld.de

Last modified: Thu Jun 9 14:11:14 CEST 2005