Course schedule and exercises
The following plan is preliminary, and there will probably be some changes to it.
| Date | Topic | Exercises |
|---|---|---|
| Wednesday 20.8 | Introduction, categories | Intro |
| Friday 22.8 | Categories | Exercise set 1, Hints |
| Wednesday 27.8 | Functors, natural transformations | |
| Friday 29.8 | Yoneda lemma, equivalence of categories | |
| Wednesday 3.9 | Adjoint functors | |
| Friday 5.9 | Limits and colimits | |
| Wednesday 10.9 | Additive categories, kernels and cokernels | Exercise set 2, Hints |
| Friday 12.9 | Abelian categories, exact sequences | |
| Wednesday 17.9 | Exact sequences, pullbacks and pushouts, some diagram lemmas | |
| Friday 19.9 | Some diagram lemmas | Exercise set 3, Hints |
| Wednesday 24.9 | Exact functors, the Hom-functor, projective and injective objects | |
| Friday 26.9 | Tensor products | |
| Wednesday 1.10 | Tensor products, complexes, homology | |
| Friday 3.10 | The long exact sequence in homology | |
| Wednesday 8.10 | The cone construction, quasi-isomorphisms | Exercise set 4, Hints |
| Friday 10.10 | Homotopy category, projective and injective resolutions | |
| Wednesday 15.10 | The horseshoe lemma, derived functors | |
| Friday 17.10 | Derived functors, Ext and Tor | |
| Wednesday 22.10 | Dimension shifting, double complexes, balancing Ext | |
| Friday 24.10 | Balancing Ext | |
| Wednesday 29.10 | Homological dimension | |
| Friday 31.10 | Triangulated categories | Exercise set 5, Hints |
| Wednesday 5.11 | Properties of triangulated categories, the homotopy category | |
| Friday 7.11 | Triangulated structure of the homotopy category | |
| Wednesday 12.11 | The derived category | |
| Friday 14.11 | The derived category, interpretations of Ext, morphisms in the derived category | |
| Wednesday 19.11 | Interpretations of Ext | |
| Friday 21.11 | Repetition, some directions beyond ma3204 |