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- W2968868063 abstract "These are the notes of three lectures given in the International Workshop on Noncommutative Geometry held in I.P.M., Tehran, Iran, September 11-22. The first lecture is an introduction to the basic notions of abelian category theory, with a view toward their algebraic geometric incarnations (as categories of modules over rings or sheaves of modules over schemes). In the second lecture, we motivate the importance of chain complexes and work out some of their basic properties. The emphasis here is on the notion of cone of a chain map, which will consequently lead to the notion of an exact triangle of chain complexes, a generalization of the cohomology long exact sequence. We then discuss the homotopy category and the derived category of an abelian category, and highlight their main properties. As a way of formalizing the properties of the cone construction, we arrive at the notion of a triangulated category. This is the topic of the third lecture. After presenting the main examples of triangulated categories (i.e., various homotopy/derived categories associated to an abelian category), we discuss the problem of constructing abelian categories from a given triangulated category using t-structures." @default.
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- W2968868063 date "2007-04-01" @default.
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- W2968868063 title "Lectures on derived and triangulated categories" @default.
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