Abstract
The purpose of these notes is to provide enough background information to define triangulated categories. We provide background information on monomorphisms, epimorphisms, kernels and cokernels. We use this information to define additive and abelian categories, and provide several examples. We give a full definition of triangulated categories and the axioms TR1–TR4. We conclude by describing some basic results on triangulated categories, leading to a long exact sequence of morphism groups.
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CITATION STYLE
Hanratty, C. (2018). Abelian and triangulated categories. In Springer Proceedings in Mathematics and Statistics (Vol. 240, pp. 3–16). Springer New York LLC. https://doi.org/10.1007/978-3-319-91626-2_1
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