# Given undergraduate Algebra background, which introductory Homological Algebra textbook?

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?

• do you know what $R$-modules are? What is an exact sequence? – Riccardo Dec 7 '15 at 10:48
• you can try Weibel, but $2$ weeks seems a very short time, I mean, it really depends what you mean by "having a comprehensive picture" of homological algebra. Let me make an example. Spectral sequences, a central tool in homological algebra. It's not so easy understanding them (i.e. doing some easy calculations) in a very short time. – Riccardo Dec 7 '15 at 10:54
• I didn't read it, but the point of my comment is that for any book you can think of, $2$ weeks is a very short time. I mean, it really depends what you mean by a comprehensive look on hom. algebra. Surely you need some Cat-Theory, and if u never see it, then it'd take some time. – Riccardo Dec 7 '15 at 10:58
• I think that your best option would be to start reading Weibel, and try to integrate "unknown" concepts whenever you meet them. And do most of the exercise you'll encounter (especially in the Spectral Sequence chapter) . Only in this way you'll get used to the machinery behind it. But as far as I can tell you, it'll take way more than 2 weeks. – Riccardo Dec 7 '15 at 11:06
• I think these topics are dealt in Weibel. Start reading Weibel, and integrate whenever you feel you don't understand. Weibel (with the right prerequisites) is not a difficult book. Try to read it :) – Riccardo Dec 7 '15 at 11:24