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Can someone give me a recommendation on homological algebra textbooks? I would like something that are accessible to beginners and that have

1) a brief look at preadditive, additive, monoidal, abelian, triangulated categories (hopefully without going too far),

2) a good motivation from algebraic topology exploited,

3) an extensive 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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Weibel covers almost everything you mention, except for monoidal categories. – Zhen Lin Jan 30 '14 at 10:54
For (basic) monoidal categories theory and applications I recommend Kassel's "Quantum Groups". If you want to dive into homological algebra starting from alg. topology, then pick up Gelfand Manin's textbook. – Avitus Jan 30 '14 at 11:31
@Zhen Lin: Thank you! I will have a look at Weibel. – eltonjohn Jan 31 '14 at 14:36
@Avitus: Thank you. By the way I understand there are two books on homological algebra by Gelfand and Manin. Is it correct that you are referring to "Methods of Homological Algebra"? – eltonjohn Jan 31 '14 at 14:40
you are right @eltonjohn; I meant the "Methods". – Avitus Jan 31 '14 at 14:48

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