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