Lecture plan and exercises

This the material covered in the course. It follows mostly the structure of the notes by Steffen Oppermann.

Exercises will be posted here every week. You will be expected to have worked on them before the next exercise session, which will be held in class during the last hour of the Monday lecture.

Week Monday Friday Exercises
34 Introduction Categories: definition, functors
35 No Lecture Categories: natural transformations, equivalences of categories
36 Categories: equivalence of categories Categories: adjoint functors, limits Exercise session 1
37 Categories: limits and adjoint functors Additive and abelian categories: definitions, kernels and cokernels Exercise session 2
38 Additive and abelian categories: exact sequences Additive and abelian categories: pullbacks and pushouts Exercise session 3
39 Additive and abelian categories: diagram lemmas Hom and tensor products: definitions, projectives and injectives
40 Hom and tensor products: hom-tensor adjunction Morita theory: progenerators Exercise session 4
41 Morita theory: Eilenberg-Watts theorem, Morita theorems Complexes and homology: definitions, long exact sequence Exercise session 5
42 Complexes and homology: homotopy Complexes and homology: cones and quasi-isomorphisms Exercise session 6
43 Complexes and homology: projective and injective resolutions Derived functors: definitions Exercise session 7
44 Derived functors: first properties Derived functors: syzygies and dimension shift, Yoneda extensions Exercise session 8
45 Derived functors: balancing Tor and Ext Triangulated categories: definitions Exercise session 9
46 Triangulated categories: homotopy categories Triangulated categories: derived categories, localisation
47 Derived categories: Hom(A,B[n]) Derived categories: derived functors Exercise session 10
48 Extra Lecture: Big exercise session No Lecture Exercise session 11
2018-11-16, louispht