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Relative Homological Algebra and Purity in Triangulated Categories

✍ Scribed by Apostolos Beligiannis

Publisher
Elsevier Science
Year
2000
Tongue
English
Weight
626 KB
Volume
227
Category
Article
ISSN
0021-8693

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✦ Synopsis

CONTENTS 1. Introduction. 2. Proper classes of triangles and phantom maps. 3. The Steenrod and Freyd category of a triangulated category. 4. Projecti¨e objects, resolutions, and deri¨ed functors. 5. The phantom tower, the cellular tower, homotopy colimits, and compact objects. 6. Localization and the relati¨e deri¨ed category. 7. The stable triangulated category. 8. Projecti¨ity, injecti¨ity, and flatness. 9. Phantomless triangulated categories. 10. Brown representation theorems. 11. Purity. 12. Applications to deri¨ed and stable categories. References.

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