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I have read the answers here and here and need to ask something more.

I wish to study the book on Homological Algebra by Weibel but am not sure of the prerequisites. In particular how much category theory is assumed on the part of the reader ?

Would prerequisites for Rotman's book be lesser ? Should I prefer Rotman's book over Weibel's ?

I am more interested in applying Homological Algebra to Topology & Geometry rather than other applications.

My background is 1 year graduate course on Algebra based on Lang covering Groups, Rings, Modules, Fields & Galois Theory and basics of Homological Algebra. I do not know any algebraic topology beyond the definition of fundamental group. But I do not mind postponing understanding the motivation for some concepts of Homological Algebra that may have origin in Topology.

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    $\begingroup$ Weibel includes an introduction to category theory as an appendix, as well as defining and explaining categorical constructions as they are used. I have heard that it is more intense than Rotman's notes, but cannot say for myself. $\endgroup$ – Harry Wilson Nov 21 '13 at 15:47
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    $\begingroup$ I dont think u need a much more background. Weibel is great book but it requires more maturity from readers a lot is left to prove in exercise. In Rotman everything is proved sometimes couple of times in a different way with all details. I think it wouldnt be bad idea to read Waibel and if you have problems confront material with Rotman. $\endgroup$ – user52045 Nov 21 '13 at 16:01
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You definitely have enough prerequisites to read Weibel, especially since you've already seen some basic homological algebra. The toughest part in terms of category theory for you might actually be getting used to abelian categories, but in most places you don't actually need to work directly with abelian categories, and you can use the embedding theorem (so essentially you prove things as if you were in the category of modules). So category theory probably won't be a block for you.

The good thing about Rotman is that he has more material on specific examples, and he goes into more detail.

Ultimately I recommend reading Weibel's book (however, as a disclaimer I have only read Weibel and just glanced at Rotman). Reading Rotman you will have gone through nearly seven hundred pages (Weibel: 415) and still not have seen Lie algebra homology, Hochschild and cyclic homology, and perhaps most importantly for someone who might be interested in topology, simplicial methods (the highlight of which is the Dold-Kan correspondence). To me this seems unacceptable. Rotman also places the chapter on spectral sequences at the end of the book and thus you don't get much of a chance to use them throughout the other chapters, such as group cohomology.

Finally, although Weibel's book has exercises, you might want to supplant them with a few more from either Rotman or Hilton and Stammbach.

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  • $\begingroup$ Thanks a lot ! Is there any specific reference on Abelian Categories that I might find helpful ? $\endgroup$ – user90041 Nov 22 '13 at 14:00
  • $\begingroup$ If you need a specific reference you could try Carl Faith's book Algebra (vol 1). $\endgroup$ – user2055 Nov 22 '13 at 14:13
  • $\begingroup$ Hi @JasonPolak , my question is almost same as OP. So instead of creating another question, I am asking it here. I have read groups, vector spaces, rings, fields (excluding Galois theory) from Herstein's Topic's in Algebra, and boundaries, chains, simplexes, stokes theorem from Rudin's Mathematical Analysis. Do I have enough prerequisites to start reading Weibel's book? $\endgroup$ – Sayan Nov 28 '14 at 14:16
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    $\begingroup$ @Sayan: I think you probably do have enough. However, Herstein's book doesn't have much module theory, so if you find the going a bit tough you could keep a book on modules at hand. For instance, the treatment of projective and injective modules in Weibel is a bit terse, and some of the constructions could seem a bit unmotivated if you've not seen many examples of modules before. $\endgroup$ – user2055 Nov 28 '14 at 17:56

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