Lectures on Homological Algebra
The pdf files below are lecture notes from a course on Homological Algebra
which I gave at the University of Western Ontario during
the Fall term of 2009.
The notes are still subject to
change - the indicated dates are last updates.
If you have comments or suggestions about these files, please do not
hesitate to contact me: firstname.lastname@example.org.
- Lecture 01: Chain complexes, exactness, simplicial sets
- Lecture 02: Chain complex homotopy theory, model categories
- Lecture 03: Chain homotopy, homotopical algebra
- Lecture 04: Torsion products: basic theory
- Lecture 05: Tensor product of chain complexes
- Lecture 06: Cohomology, injective resolutions, Eilenberg-Cartan resolutions
- Lecture 07: Spectral sequences: an introduction
- Lecture 08: Dold-Kan correspondence, model structures for simplicial modules
- Lecture 09: Homotopy colimits, cosimplicial chain complexes
- Lecture 10: Bisimplicial modules, bisimplicial sets, Serre spectral sequence, some calculations