Course schedule and lecture notes
The plan is that the last hour on every second Wednesday will be devoted to solving exercises. They will be based on the material covered in the previous weeks.
| Date | Subject | Notes | Exercises |
|---|---|---|---|
| Mon 22 Aug | No Lecture | ||
| Wed 24 Aug | Introduction, Categories | notes | |
| Mon 29 Aug | Categories, Functors | notes | |
| Wed 31 Aug | Natural transformations, Yoneda lemma | notes | Exercise set 1 Hints |
| Mon 05 Sep | Equivalence of categories, Adjoint functors | notes | |
| Wed 07 Sep | Adjoint functors, Limits and Colimits | notes | |
| Mon 12 Sep | Additive Categories, Kernels and Cokernels | notes | |
| Wed 14 Sep | Abelian Categories, Exact Sequences | notes | Exercise set 2 Hints |
| Mon 19 Sep | Exact sequences, Pushouts and Pullbacks | notes | |
| Wed 21 Sep | Some diagram lemmas, Exact functors | notes | |
| Mon 26 Sep | Projective and Injective objects, Tensor products | notes | |
| Wed 28 Sep | Tensor products | notes | Exercise set 3 Hints |
| Mon 03 Oct | Tensor Products, Complexes, Long Exact Sequence in Homology | notes | |
| Wed 05 Oct | The Cone Construction, The Homotopy Category | notes | |
| Mon 10 Oct | Homotopy category, Projective and Injective Resolutions | notes | |
| Wed 12 Oct | The Horseshoe Lemma, Derived Functors | notes | Exercise set 4 Hints |
| Mon 17 Oct | Derived Functors, Ext and Tor | notes | |
| Wed 19 Oct | Dimension Shifting, Double Complexes | notes | |
| Mon 24 Oct | Balancing Ext, Homological Dimension | notes | |
| Wed 26 Oct | Homological Dimension | notes | Exercise set 5 Hints |
| Mon 31 Oct | Triangulated categories | notes | |
| Wed 02 Nov | Properties of triangulated categories, Triangulated structure of Homotopy category | notes | |
| Mon 07 Nov | Derived functors and homotopy category, Ore condition I | notes | Exercise set 6 Hints |
| Wed 09 Nov | Ore condition II, The Derived category | notes | |
| Mon 14 Nov | Triangulated structure of the Derived category | notes | |
| Wed 16 Nov | Morphisms in the Derived category, Derived functors | notes | |
| Mon 21 Nov | Repetition | notes | Exercise set 7 Hints |
| Wed 23 Nov | No Lecture |