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I'm not a physicist, what I wrote was explained to me by a physicist. He shared his wish. I do think that the written one look really to the one that the physicists wants. In a mathematical text book, it is more about what is convenient for mathematicians, and I'm not sure that is has something to do with what physicists are looking for.
@user40276 Thanks for the link, In some article of ncatlab I can't see what is really important about a subject, at the end I get more confused :). Anyway, I did notice that the functorial (categorical) approach looks useless.. I was looking for another opinion about this subject.
