### Algebraic versus topological triangulated categoriesAlgebraic versus topological triangulated categories

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 Author Schwede, Stefan Source arXiv.org Content type Text File Format PDF Date of Submission 2008-07-16 Language English
 Subject Domain (in DDC) Natural sciences & mathematics ♦ Mathematics Subject Keyword Mathematics - Algebraic Topology ♦ 55P42 ♦ math Abstract The most commonly known triangulated categories arise from chain complexes in an abelian category by passing to chain homotopy classes or inverting quasi-isomorphisms. Such examples are called algebraic' because they originate from abelian (or at least additive) categories. Stable homotopy theory produces examples of triangulated categories by quite different means, and in this context the source categories are usually very non-additive' before passing to homotopy classes of morphisms. Because of their origin I refer to these examples as `topological triangulated categories'. In these extended talk notes I explain some systematic differences between these two kinds of triangulated categories. There are certain properties -- defined entirely in terms of the triangulated structure -- which hold in all algebraic examples, but which fail in some topological ones. These differences are all torsion phenomena, and rationally there is no difference between algebraic and topological triangulated categories. Description Reference: Triangulated categories, 389--407, London Mathematical Society Lecture Notes 375, Cambridge University Press, 2010 Educational Use Research Learning Resource Type Article