Triangulated categories / by Amnon Neeman.

Format:

Book

Author/Creator:

Neeman, Amnon, author.

Series:

Annals of mathematics studies ; Number 148.

Annals of Mathematics Studies ; Number 148

Language:

English

Subjects (All):

Categories (Mathematics).

Physical Description:

1 online resource (461 p.)

Edition:

1st ed.

Place of Publication:

Princeton, New Jersey : Princeton University Press, 2001.

Language Note:

English

Summary:

The first two chapters of this book offer a modern, self-contained exposition of the elementary theory of triangulated categories and their "ients. 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.

Contents:

Front matter

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 (Sop, Ab)

Chapter 7. Homological properties of Εx(Sop,Αb)

Chapter 8. Brown representability

Chapter 9. Bousfield localisation

Appendix A. Abelian categories

Appendix B. Homological functors into [AB5α] categories

Appendix C. Counterexamples concerning the abelian category A(Τ)

Appendix D. Where Τ is the homotopy category of spectra

Appendix E. Examples of non-perfectly-generated categories

Bibliography

Index

Notes:

Description based upon print version of record.

Includes bibliographical references and index.

Description based on print version record.

ISBN:

0-691-08685-0

1-4008-3721-9

OCLC:

888743941