Lectures on Homological Algebra

J.F. Jardine

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 jardine@uwo.ca.

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