Topological triangulated categories

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TOPOLOGICAL TRIANGULATED CATEGORIES STEFAN SCHWEDE Many triangulated categories arise from chain complexes in an additive or abelian category by passing to chain homotopy classes or inverting quasi-isomorphisms. Such examples are called ‘algebraic' because they have underlying additive categories. Stable homotopy theory produces examples of triangulated categories by quite different means, and in this context the underlying categories are usually very ‘non-additive' before passing to homotopy classes of morphisms. We call such triangulated categories topological, and formalize this in Definition 1.4 via homotopy categories of stable cofibration categories.

• adjunction unit
• triangulated categories
• unit cycles
• abelian category
• morphism chain complexes
• cofibration category
• homotopy category
• complexes
• category
• structure