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2018 | OriginalPaper | Chapter

Abelian and Triangulated Categories

Author : Chantelle Hanratty

Published in: Superschool on Derived Categories and D-branes

Publisher: Springer International Publishing

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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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next chapter Derived Categories and Derived Functors
Literature
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Krishnan, V.S.: An introduction to category theory. North-Holland Publishing Co., New York-Amsterdam (1981)
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Verdier, J.L.: Des catégories dérivées des catégories abéliennes. Astérisque (239), xii+253 pp. (1997) (1996). With a preface by Luc Illusie, Edited and with a note by Georges Maltsiniotis
Metadata
Title
Abelian and Triangulated Categories
Author
Chantelle Hanratty
Copyright Year
2018
Book
Superschool on Derived Categories and D-branes

Print ISBN: 978-3-319-91625-5

Electronic ISBN: 978-3-319-91626-2

Copyright Year: 2018

DOI
https://doi.org/10.1007/978-3-319-91626-2_1

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