an:06272690
Zbl 1294.18008
Schwede, Stefan
The \(p\)-order of topological triangulated categories
EN
J. Topol. 6, No. 4, 868-914 (2013).
00330235
2013
j
18E30 55P42
topological triangulated category; cofibration category; model category; \(p\)-order of triangulated category
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.
Alexander Zimmermann (Amiens)