Recently I thought that maybe is a good time to try, read Grothendieck's "Tohoku paper" as a sort of inspiration for the future and to read some of the ideas of this great mathematician, which (among many of course) indisputably is one of the most inspired papers in contemporary algebra (and not only). However, because the subject is quite difficult even for experts I was thinking that maybe a book would be necessery for definitions, comments or even examples on some of the notions that this paper includes. Also, I found a translated from French to English version (by Michael Barr) and I think that is the only one that exists. Is this version the "official" or there are others?

Also, do you know if there is any book that might help me on that? Or any other papers towards that direction, that might be helpful as well?

  • $\begingroup$ (1) The translation is about as official as we're likely to get. It's made by someone who knows what he's talking about. (2) Basically any good book on homological algebra will be a good help. Grothendieck seems to have preferred Godement's book for this. There should be a MathOverflow thread with lots of suggestions. Weibel's book is really popular. The one thing I'm not sure about is a good reference for $G$-sheaves, but worry about that when you get there. $\endgroup$ – Hoot Jul 1 '16 at 17:47
  • $\begingroup$ thank you for your response. I am sure that it would get me a long long time to finish it and of course more time to understand some things. However, I am quite sure that it worths. To be honest, I was thinking something more contemporary than Godement;s book. But I am not sure. $\endgroup$ – user321268 Jul 1 '16 at 17:57
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    $\begingroup$ Why not study homological algebra from some a source intended to be used in that way? There are quite a few good textbooks. $\endgroup$ – Mariano Suárez-Álvarez Jul 4 '16 at 15:24
  • $\begingroup$ @MarianoSuárez-Alvarez thank you for your comment, except the "usuals" (and this is quite subjective presumably) can you tell me a couple of them? $\endgroup$ – user321268 Jul 5 '16 at 6:25
  • $\begingroup$ @mayer_vietoris no the usuals is not subjective, there are standard books.. even google knows this $\endgroup$ – syzygy Jul 9 '16 at 17:55

As far as I know, there is no other translation. However, you should know that there were two translators, the other being Marcia L. Barr. She is a professional French/English translator and I put it into mathematicese. Very much against G's wishes; otherwise it would have appeared as TAC reprint.

As for your question, in 1957 category theory wasn't even a thing. I suppose Godement's book is as good a place to begin as any. I would also recommend Cartan-Eilenberg. The Tohoku paper and Dan Kan's discovery of adjoints are what put CT on the map.


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