Lectures on Homological Algebra
The links below are to lecture notes from a course on Homological Algebra which I gave at the University of Western Ontario during the Fall term of 2009.
If you have comments or suggestions about these files, please do not hesitate to contact me at 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