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Cohomologically triangulated categories I

Published online by Cambridge University Press:  03 January 2008

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

We introduce cohomologically triangulated categories as triples (A,t,▽) given by an additive category A, an additive equivalence t:AA and a cohomology class ▽ in the translation cohomology H3(A,t). A stable homotopy theory C with A = HoC yields such a triple and the class of distinguished triangles in A is deduced from ▽.

Keywords

triangulated categoriespretriangulated categoriesgroupoid-enriched categories

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Type
Research Article
Information
Journal of K-Theory , Volume 1 , Issue 1 , February 2008 , pp. 3 - 48
Copyright
Copyright © ISOPP 2008

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