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Triangulated categories: definitions, properties, and examples. (English) Zbl 1221.18008
Holm, Thorsten (ed.) et al., Triangulated categories. Based on a workshop, Leeds, UK, August 2006. Cambridge: Cambridge University Press (ISBN 978-0-521-74431-7/pbk). London Mathematical Society Lecture Note Series 375, 1-51 (2010).
This article presents a quick and readable overview of triangulated categories for a beginner. It begins with some historical background and then gives the definition of a triangulated category with proper motivation. All basic properties of a triangulated category are derived. The two examples that are discussed in great length are the derived category of an abelian category and the stable category.
For the entire collection see [Zbl 1195.18001].

MSC:
18E30 Derived categories, triangulated categories (MSC2010)
18-02 Research exposition (monographs, survey articles) pertaining to category theory
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