Triangulated Categories. (AM-148)

Triangulated Categories. (AM-148)

by Amnon Neeman
     
 

ISBN-10: 0691086869

ISBN-13: 9780691086866

Pub. Date: 01/03/2001

Publisher: Princeton University Press

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,

Overview

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.

Product Details

ISBN-13:
9780691086866
Publisher:
Princeton University Press
Publication date:
01/03/2001
Series:
Annals of Mathematics Studies Series
Pages:
449
Product dimensions:
6.12(w) x 9.24(h) x 1.10(d)

Table of Contents

Contents

0. Acknowledgements, 3,
1. Introduction, 3,
Chapter 1. Definition and elementary properties of triangulated categories, 29,
Chapter 2. Triangulated functors and localizations of triangulated categories, 73,
Chapter 3. Perfection of classes, 103,
Chapter 4. Small objects, and Thomason's localisation theorem, 123,
Chapter 5. The category A(S), 153,
Chapter 6. The category [xi]x (Sop, Ab), 183,
Chapter 7. Homological properties of [xi]x(Sop, Ab), 221,
Chapter 8. Brown representability, 273,
Chapter 9. Bousfield localisation, 309,
Appendix A. Abelian categories, 321,
Appendix B. Homological functors into [AB5α] categories, 369,
Appendix C. Counterexamples concerning the abelian category A(T), 387,
Appendix D. Where T is the homotopy category of spectra, 407,
Appendix E. Examples of non-perfectly-generated categories, 427,
Bibliography, 443,
Index, 445,

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