Course schedule and lecture notes
The last hour on every second Thursday will be devoted to solving exercises. They will be based on the material covered in the previous weeks.
The following plan is preliminary, and there will probably be some changes to it.
| Date | Subject | Notes | Exercises |
|---|---|---|---|
| Tue 22 Aug | Introduction, Categories | notes | |
| Thu 24 Aug | Categories, Functors | notes | |
| Tue 29 Aug | Natural transformations, Yoneda lemma | notes | Exercise set 1 Hints |
| Thu 31 Aug | Equivalence of categories, Adjoint functors | notes | |
| Tue 05 Sep | Adjoint functors, Limits and Colimits | notes | |
| Thu 07 Sep | Additive Categories, Kernels and Cokernels | notes | |
| Tue 12 Sep | Abelian Categories, Exact Sequences | notes | Exercise set 2 Hints |
| Thu 14 Sep | Exact sequences, Pushouts and Pullbacks | notes | |
| Tue 19 Sep | Some diagram lemmas, Exact functors | notes | |
| Thu 21 Sep | Projective and Injective objects, Tensor products | notes | |
| Tue 26 Sep | Tensor products | notes | Exercise set 3 Hints |
| Thu 28 Sep | Tensor Products, Complexes, Long Exact Sequence in Homology | notes | |
| Tue 03 Oct | The Cone Construction, The Homotopy Category | notes | |
| Thu 05 Oct | Homotopy category, Projective and Injective Resolutions | notes | |
| Tue 10 Oct | The Horseshoe Lemma, Derived Functors | notes | Exercise set 4 Hints |
| Thu 12 Oct | Derived Functors, Ext and Tor | notes | |
| Tue 17 Oct | Dimension Shifting, Double Complexes | notes | |
| Thu 19 Oct | Balancing Ext, Homological Dimension | notes | |
| Tue 24 Oct | Homological Dimension | notes | Exercise set 5 Hints |
| Thu 26 Oct | Triangulated categories | notes | |
| Tue 31 Oct | Properties of triangulated categories, The Homotopy category | notes | |
| Thu 02 Nov | Triangulated structure of the Homotopy category, Derived functors | notes | Exercise set 6 Hints |
| Tue 07 Nov | Localizations of categories, The Derived category | notes | |
| Thu 09 Nov | Localizations of (additive) categories | notes | |
| Tue 14 Nov | Triangulated structure of the Derived category, Morphisms in the Derived category | notes | |
| Thu 16 Nov | Morphisms in the Derived category, Repetition. | notes | Exercise set 7 Hints |
| Tue 21 Nov | Repetition | ||
| Thu 23 Nov |