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Cohomologically triangulated categories II

Published online by Cambridge University Press:  01 December 2008

H.-J. Baues  and
F. Muro
H.-J. Baues
Affiliation:
Max-Planck-Institut für Mathematik, Vivatsgasse 7, 53111 Bonn, Germany, baues@mpim-bonn.mpg.de.
F. Muro
Affiliation:
Universitat de Barcelona, Departament d'Àlgebra i Geometria, Gran via de les corts catalanes 585, 08007 Barcelona, Spain, fmuro@ub.edu.
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Abstract

A cohomologically triangulated category is an additive category A together with a translation functor t and a cohomology class Δ ∈ H3(A,t) such that any good translation track category representing Δ is a triangulated track category. In this paper we give purely cohomological conditions on Δ which imply that (A,t,Δ) is a cohomologically triangulated category, avoiding the use of track categories. This yields a purely cohomological characterization of triangulated cohomology classes.

Keywords

triangulated categoriespretriangulated categoriescohomology of categories

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Type
Research Article
Information
Journal of K-Theory , Volume 3 , Issue 1 , February 2009 , pp. 1 - 52
Copyright
Copyright © ISOPP 2009

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