Triangulated Category
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High Quality Content by WIKIPEDIA articles! A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t-category, though similarly named, refers to a more specific concept. The notion of a derived category was introduced by Jean-Louis Verdier (1963) in his Ph.D. thesis, based on the ideas of Grothendieck. He also defined the notion of a triangulated category, based upon the observation that a derived category had some special "triangles", by writing down…mehr

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High Quality Content by WIKIPEDIA articles! A triangulated category is a mathematical category satisfying some axioms that are based on the properties of the homotopy category of spectra, and the derived category of an abelian category. A t-category, though similarly named, refers to a more specific concept. The notion of a derived category was introduced by Jean-Louis Verdier (1963) in his Ph.D. thesis, based on the ideas of Grothendieck. He also defined the notion of a triangulated category, based upon the observation that a derived category had some special "triangles", by writing down axioms for the basic properties of these triangles. A very similar set of axioms was written down at about the same time by Dold and Puppe (1961).