I am attending a course in Homological Algebra this semester, in the following special topics. I know that there are similar posts, but in this post I specifically ask to recommend me a combination of well written books or notes, with plenty of worked examples in the following topics:
- General Theory of Categories
- Adjoint Functors and Limits
- Abelian Categories
- Hom and Tensor Functors
- Projective and Injective Objects
- Cosets and Homology
- The long exact sequence in Homology
- Cone and quasi-isomorphisms
- Homotopy projective and injective resolution
- Derived Functors, $Ext^1$ and Extensions
- Homological dimensions
- The homotopy category is triangular
- Derived Categories and Derived Functors
- $Ext$ as set of morphisms in derived category
- Derived Equivalences
Also, in this course, the suggested bibliography is the following :
A. J. Berrick, Michael E. Keating, Categories and Modules with K-theory in view.
Sergei I. Gelfand, Yuri I. Manin: Methods of Homological Algebra.
Peter J. Hilton, Urs Stammbach: A Course in Homological Algebra.
Joseph J. Rotman: An Introduction to Homological Algebra.
Charles A. Weibel: An Introduction to Homological Algebra.
Could you please provide me some useful information about these books?
Thank you in advance.