Homology / by Saunders Mac Lane
(Classics in Mathematics ; 114)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | Berlin, Heidelberg : Springer Berlin Heidelberg , 1995 |
| 本文言語 | 英語 |
| 大きさ | X, 422 p : online resource |
書誌詳細を非表示
| 内容注記 | I. Modules, Diagrams, and Functors 1. The Arrow Notation 2. Modules 3. Diagrams 4. Direct Sums 5. Free and Projective Modules 6. The Functor Horn 7. Categories 8. Functors II. Homology of Complexes 1. Differential Groups 2. Complexes 3. Cohomology 4. The Exact Homology Sequence 5. Some Diagram Lemmas 6. Additive Relations 7. Singular Homology 8. Homotopy 9. Axioms for Homology III. Extensions and Resolutions 1. Extensions of Modules 2. Addition of Extensions 3. Obstructions to the Extension of Homomorphisms 4. The Universal Coefficient Theorem for Cohomology 5. Composition of Extensions 6. Resolutions 7. Injective Modules 8. Injective Resolutions 9. Two Exact Sequences for Extn 10. Axiomatic Description of Ext 11. The Injective Envelope IV. Cohomology of Groups 1. The Group Ring 2. Crossed Homomorphisms 3. Group Extensions 4. Factor Sets 5. The Bar Resolution 6. The Characteristic Class of a Group Extension 7. Cohomology of Cyclic and Free Groups 8. Obstructions to Extensions 9. Realization of Obstructions 10. SCHUR’S Theorem 11. Spaces with Operators V. Tensor and Torsion Products 1. Tensor Products 2. Modules over Commutative Rings 3. Bimodules 4. Dual Modules 5. Right Exactness of Tensor Products 6. Torsion Products of Groups 7. Torsion Products of Modules 8. Torsion Products by Resolutions 9. The Tensor Product of Complexes 10. The KÜNNETH Formula 11. Universal Coefficient Theorems VI. Types of Algebras 1. Algebras by Diagrams 2. Graded Modules 3. Graded Algebras 4. Tensor Products of Algebras 5. Modules over Algebras 6. Cohomology of free Abelian Groups 7. Differential Graded Algebras 8. Identities on Horn and ? 9. Coalgebras and HOPF Algebras VII. Dimension 1. Homological Dimension 2. Dimensions in Polynomial Rings 3. Ext and Tor for Algebras 4. Global Dimensions of Polynomial Rings 5. Separable Algebras 6. Graded Syzygies 7. Local Rings VIII. Products 1. Homology Products 2. The Torsion Product of Algebras 3. A Diagram Lemma 4. External Products for Ext 5. Simplicial Objects 6. Normalization 7. Acyclic Models 8. The EILENBERG-ZILBER Theorem 9. Cup Products IX. Relative Homological Algebra 1. Additive Categories 2. Abelian Categories 3. Categories of Diagrams 4. Comparison of Allowable Resolutions 5. Relative Abelian Categories 6. Relative Resolutions 7. The Categorical Bar Resolution 8. Relative Torsion Products 9. Direct Products of Rings X. Cohomology of Algebraic Systems 1. Introduction 2. The Bar Resolution for Algebras 3. The Cohomology of an Algebra 4. The Homology of an Algebra 5. Homology of Groups and Monoids 6. Ground Ring Extensions and Direct Products 7. Homology of Tensor Products 8. The Case of Graded Algebras 9. Complexes of Complexes 10. Resolutions and Constructions 11. Two-stage Cohomology of DGA-Algebras 12. Cohomology of Commutative DGA-Algebras 13. Homology of Algebraic Systems XI. Spectral Sequences 1. Spectral Sequences 2. Fiber Spaces 3. Filtered Modules 4. Transgression 5. Exact Couples 6. Bicomplexes 7. The Spectral Sequence of a Covering 8. Cohomology Spectral Sequences 9. Restriction, Inflation, and Connection 10. The Lyndon Spectral Sequence 11. The Comparison Theorem XII. Derived Functors 1. Squares 2. Subobjects and Quotient Objects 3. Diagram Chasing 4. Proper Exact Sequences 5. Ext without Projectives 6. The Category of Short Exact Sequences 7. Connected Pairs of Additive Functors 8. Connected Sequences of Functors -- 9. Derived Functors -- 10. Products by Universality -- 11. Proper Projective Complexes -- 12. The Spectral KÜNNETH Formula -- List of Standard Symbols |
|---|---|
| 一般注記 | 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 |
| 著者標目 | *Mac Lane, Saunders author SpringerLink (Online service) |
| 件 名 | LCSH:Mathematics LCSH:Category theory (Mathematics) LCSH:Homological algebra FREE:Mathematics FREE:Category Theory, Homological Algebra |
| 分 類 | DC23:512.6 |
| 巻冊次 | ISBN:9783642620294 
|
| ISBN | 9783642620294 |
| URL | http://dx.doi.org/10.1007/978-3-642-62029-4 |
目次／あらすじ
類似資料
この資料を見た人はこんな資料も見ています
この資料の利用統計
このページへのアクセス回数：1回
※2021年9月12日以降