I have read the answer for graduate-level Algebra background and all answers in stackexchange and mathoverflow discussing Homological Algebra textbooks. But none of them directly answers my question, and not all of the lauded textbooks indicates the prerequisites clearly.
My background: undergraduate Algebra (until the beginning of ring theory in Dummit's 'Abstract Algebra'), undergraduate Topology (Munkres' 'Topology' and Armstrong 'Basic Topology'), graduate differential geometry.
My aim is to
- Get a big, comprehensive picture of Homological Algebra
- in 2-week time,
- , and preferably, through a book that explains the concepts in a quite intuitive way (because for a quick and non-rigorous read that I plan for, such material is easier to remember than a technical one)
I also plan to only read the proofs' sketch or just omit them, so perhaps books that often leave gaps in the proof or leave proofs as exercise are fine. Also, if a good book requires me to update my Algebra background slightly, i.e. knowing a few more definitions/theorems/applications, that's good enough.
I am mostly weighing between Rotman's and Weibel's. Rotman's has a fame of being introductory and readable, but here seems to say that it does not go very far, despite being lengthy. Weibel's, from the description I read, seems promising for my purpose, but the author indicates that the prerequisite is a graduate-level introductory Algebra course.
Does it require much reading to fulfill the prerequisites for Weibel's? Or is there any other option that fits with my purpose?
Methods of homological algebra by manin and gelfand. It starts off with simplicial sets and gives you an introduction to category theory in the second chapter.