Ebook: Homology
Author: Saunders Mac Lane (auth.)
- Tags: Category Theory Homological Algebra
- Series: Classics in Mathematics 114
- Year: 1963
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
In presenting this treatment of homological algebra, it is a pleasure to acknowledge the help and encouragement which I have had from all sides. Homological algebra arose from many sources in algebra and topology. Decisive examples came from the study of group extensions and their factor sets, a subject I learned in joint work with OTTO SCHIL LING. A further development of homological ideas, with a view to their topological applications, came in my long collaboration with SAMUEL ElLENBERG; to both collaborators, especial thanks. For many years the Air Force Office of Scientific Research supported my research projects on various subjects now summarized here; it is a pleasure to acknowledge their lively understanding of basic science. Both REINHOLD BAER and JOSEF SCHMID read and commented on my entire manuscript; their advice has led to many improvements. ANDERS KOCK and JACQUES RIGUET have read the entire galley proof and caught many slips and obscurities. Among the others whose sug gestions have served me well, I note FRANK ADAMS, LOUIS AUSLANDER, WILFRED COCKCROFT, ALBRECHT DOLD, GEOFFREY HORROCKS, FRIED RICH KASCH, JOHANN LEICHT, ARUNAS LIULEVICIUS, JOHN MOORE, DIE TER PUPPE, JOSEPH YAO, and a number of my current students at the University of Chicago - not to m~ntion the auditors of my lectures at Chicago, Heidelberg, Bonn, Frankfurt, and Aarhus. My wife, DOROTHY, has cheerfully typed more versions of more chapters than she would like to count. Messrs.
Content:
Front Matter....Pages I-X
Introduction....Pages 1-8
Modules, Diagrams, and Functors....Pages 8-34
Homology of Complexes....Pages 34-63
Extensions and Resolutions....Pages 63-103
Cohomology of Groups....Pages 103-138
Tensor and Torsion Products....Pages 138-172
Types of Algebras....Pages 173-200
Dimension....Pages 200-220
Products....Pages 220-248
Relative Homological Algebra....Pages 248-279
Cohomology of Algebraic Systems....Pages 280-318
Spectral Sequences....Pages 318-358
Derived Functors....Pages 358-403
Back Matter....Pages 404-422
Content:
Front Matter....Pages I-X
Introduction....Pages 1-8
Modules, Diagrams, and Functors....Pages 8-34
Homology of Complexes....Pages 34-63
Extensions and Resolutions....Pages 63-103
Cohomology of Groups....Pages 103-138
Tensor and Torsion Products....Pages 138-172
Types of Algebras....Pages 173-200
Dimension....Pages 200-220
Products....Pages 220-248
Relative Homological Algebra....Pages 248-279
Cohomology of Algebraic Systems....Pages 280-318
Spectral Sequences....Pages 318-358
Derived Functors....Pages 358-403
Back Matter....Pages 404-422
....