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The \(p\)-order of topological triangulated categories. (English) Zbl 1294.18008
Triangulated categories are called algebraic in case they are constructed by localising procedures of homotopy categories of chain complexes of additive categories. Non-algebraic triangulated categories are called topological. The purpose of the present paper is to study the concept of a \(p\)-order of a triangulated category for a prime \(p\) in case of topological triangulated categories. The main result shows that the \(p\)-order of a topological triangulated category is at most \(p-1\), and in a second paper the author shows that the \(p\)-order of an algebraic triangulated category is always infinite. The main part of the paper defines and studies so-called cofibration categories, which are defined by a variant of Quillen’s axiom of a model category. The proof of the main result then passes to the homotopy category of so-called stable cofibration categories. An appendix gives a detailed construction of the homotopy category of a stable cofibration category and a proof that this category then is triangulated.

MSC:
18E30 Derived categories, triangulated categories (MSC2010)
55P42 Stable homotopy theory, spectra
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