Triangulated Categories

Amnon Neeman

• Publisher: Princeton University Press
• Year: 2014
• Print ISBN: 9780691086866, 9780691086859
• eBook ISBN: 9781400837212
• Topic: Mathematics
• Subtopic: Abstract Algebra
• Index: Mathematics

The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their quotients. The simple, elegant presentation of these known results makes these chapters eminently suitable as a text for graduate students. The remainder of the book is devoted to new research, providing, among other material, some remarkable improvements on Brown's classical representability theorem. In addition, the author introduces a class of triangulated categories"--the "well generated triangulated categories"--and studies their properties. This exercise is particularly worthwhile in that many examples of triangulated categories are well generated, and the book proves several powerful theorems for this broad class. These chapters will interest researchers in the fields of algebra, algebraic geometry, homotopy theory, and mathematical physics.

Table of contents

• Cover
• Title
• Copyright
• Contents
• 0. Acknowledgements
• 1. Introduction
• Chapter 1. Definition and elementary properties of triangulated categories
• Chapter 2. Triangulated functors and localizations of triangulated categories
• Chapter 3. Perfection of classes
• Chapter 4. Small objects, and Thomason's localisation theorem
• Chapter 5. The category A(S)
• Chapter 6. The category εx (S^op, Ab)
• Chapter 7. Homological properties of εx(S^op, Ab)
• Chapter 8. Brown representability
• Chapter 9. Bousfield localisation
• Appendix A. Abelian categories
• Appendix B. Homological functors into [AB5^α] categories
• Appendix C. Counterexamples concerning the abelian category A(J)
• Appendix D. Where J is the homotopy category of spectra
• Appendix E. Examples of non—perfectly—generated categories
• Bibliography
• Index