| Chapter | Section(s) | Topic | Notes | |
|---|---|---|---|---|
| 1 | Chapter I, Modules pgs. 11-25, 28 - 30 |
1. Modules 2. The group of homomorphisms 3. Sums and Products 4. Free and Projective Modules 6. Dualization, Injective Modules | ||
| 0 | Chapter II, Categories and Functors, pgs. 40-81 |
1. Categories 2. Functors 3. Duality 4. Natural Transformations 5. Products and Coproducts; Universal Constructions 6. Universal Constructions (Continued); Pull-backs and Push-outs 7. Adjoint Functors 8. Adjoint Functions and Universal Constructions 9. Abelian Categories 10. Projective, Injective, and Free Objects | ||
| 0 | Chapter IV, Derived Functors, pgs. 116-147, 156-162 |
1. Complexes 2. The Long Exact (Co)Homology Sequence 3. Homotopy 4. Resolutions 5. Derived Functors 6. The Two Long Exact Sequences of Derived Functors 7. The Functors Ext^n_A Using Projectives 8. The Functors Ext^n_A Using Injectives 10. Another Characterization of Derived Functors 11. The Functor Tor_n^A 12. Change of Rings | ||
| 0 | Chapter VIII, Exact Couples and Spectral Sequences, pgs. 255-268, 276-280, 296-305 |
1. Exact Couples and Spectral Sequences 2. Filtered Differential Objects 3. Finite Convergence Conditions for Filtered Chain Complexes 5. Limits 9. The Grothendieck Spectral Sequence | ||
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