### The characteristic cohomology class of a triangulated category , by Hans-Joachim Baues and Fernando Muro

This is the final version of a series of papers uploaded in May 25,
2005. We have splitted the long last paper of the previous version in
two parts to make it easier to understand. The results are essentially
the same, although the presentation has changed substantially. The
first three papers have not changed.

This is a collection of five papers on the foundation of triangulated
categories in the context of groupoid-enriched categories, termed
track categories, and characteristic cohomology classes. As a main
result it is shown that given an additive category A with a
translation functor t: A --> A and a class V in translation cohomology
H^3(A,t) then two simple properties of V imply that (A,t) is a
triangulated category. The cohomology class V yields an equivalence
class (B,[s]) where B is a track category with homotopy category A and
[s] is the homotopy class of a pseudofunctor s: B --> B inducing
t. The two properties of V correspond to natural axioms on B and s
which again imply that (A,t) is a triangulated category.

The five papers of this volume depend on each other by cross
references, but each paper can be read independently of the others so
that the reader is free to choose one of the papers to start. Each
paper has its own abstract, introduction and literature.

The DVI format produces errors in some diagrams.

Hans-Joachim Baues <baues@mpim-bonn.mpg.de >

Fernando Muro <muro@mpim-bonn.mpg.de >