I'm very interested in learning Homological Algebra, but I'm not sure about the prerequisites for learning it.
My current knowledge in algebra consists of Abstract Algebra (groups, rings, and fields), Linear Algebra, Galois Theory, Basic Module Theory and some introduction to Category Theory. Also I'm currently enrolled in a Commutative Algebra Course (using Atiyah's classical text).
Most of you are experts of mathematics, so, according to you, what are some great reasons to study Homological Algebra? I'd prefer that you recommend books (for self-study) as well as abstract subjects that I should learn before learning Homological Algebra. Also, what are the good texts/notes/video lectures on Homological Algebra according to my background?
Best Answer
At Cornell, we had recently a class on Homological algebra taught by Yuri Berest. I think you have enough background for reading the notes to that class. You can find them here. I think he did quite a good job of carefully going through the main basic things like abelian and triangulated categories, derived functors et.c. But at the same time, he was trying to give plenty of non-trivial examples and applications.
I helped with editing the notes, so I am sorry if I self-advertise a bit.