Triangulated categories / by Amnon Neeman.
- Princeton, New Jersey : Princeton University Press, 2001.
- Annals of mathematics studies ; Number 148.
Annals of Mathematics Studies ; Number 148
1 online resource (461 p.)
- Categories (Mathematics).
- Electronic books.
- 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.
- Front matter
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
- Description based upon print version of record.
Includes bibliographical references and index.
Description based on print version record.
- Publisher Number:
- 10.1515/9781400837212 doi
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