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Homological Algebra
"Take any book on homological algebra, and prove all the theorems without looking at the proofs given in that book. Homological algebra was invented by Eilenberg-MacLane. General category theory (i. e. the theory of arrow-theoretic results) is generally known as abstract nonsense (the terminology is due to Steenrod)."
— Serge Lang, Algebra, First edition: page 105; Second edition: page 175.
I have been using homological algebra in some of my research, so I am offering an introductory course on homological algebra during the spring semester of 2025. For details, please check this link.
Some books and reading material
The following are some textbooks and lecture notes on homological algebra.- An Introduction to Homological Algebra, by Charles A. Weibel
- Basic Homological Algebra, by M. Scott Osborne
- Methods of Homological Algebra, by Sergei I. Gelfand
- Homological Algebra, by Henri Cartan and Samuel Eilenberg
- A Course in Homological Algebra, by Peter Hilton and Urs Stammbach
- Fundamentals of Algebra: Modules, Categories, Homological Algebra, and Sheaves, by Zhi-Jie Chen
- Introduction to Categories, Homological Algebra, and Sheaf Cohomology, by Jan R. Strooker