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Can someone give me a recommendation on homological algebra textbooks? I would like something that are accessible to a beginner (i.e., someone who have studied abstract algebra) and that have

1) an account on preadditive, additive, monoidal, abelian, triangulated categories, respectively,

2) motivations from algebraic topology exploited, (an elementary example that comes into my mind is the mapping cylinder/cone construction explained in contrast with Puppe sequence,)

3) an explanation on module theoretic topics like injective / projective resolutions,

4) a coverage of sheaf theory, cohomology of groups, and Galois cohomology.

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Possible duplicate of Good introductory books on homological algebra – Watson Mar 12 at 12:52
@eltonjohn You don't close a question because you got stisfatory answers. You upvote, the useful answers you got and accept the most useful one. If your question was answered in the comments, you kindly ask if the person who answered the question could turn his comment into an answer. If, in the mean time you found the answer yourself, then you can post an answer yourself (and accept it). – gebruiker Mar 12 at 13:59
@Watson: The question looks duplicate, but (luckily for me) the answers do not. In fact the answers I got are more suited to my concern 1) through 4) above than the ones posted in…. – eltonjohn Mar 13 at 12:33
up vote 2 down vote accepted

As suggested by the OP, I move my comment into an answer with minor extensions.

Well, here we go:

For (basic) monoidal categories theory and applications I recommend Kassel's "Quantum Groups" book. If you want to dive into homological algebra starting from algebraic topology, then pick up Gelfand Manin's textbook (I refer to "Methods of Homological Algebra").

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Thanks! I browsed Gelfand and Manin. it looks very good (but a bit marred by the remaining typos that escaped revision.) --- accepted --- – eltonjohn Mar 14 at 6:49
Thank you. Yep, the book contains some typos, but doing the proofs by yourself you will be able to correct them ;) – Avitus Mar 14 at 18:40

[Weibel, An introduction to homological algebra] covers almost everything you mention, except monoidal categories.

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Thanks! My impression is Weibel is a good book except the first chapter which is too sketchy. (Of course I would not care if the book were not titled "introduction". ) --- upvoted --- – eltonjohn Mar 14 at 6:46

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