Michael Barr wrote:
I want to comment on Juergen's question. It is possible, I suppose, that Grothendieck used the phrase "dualizing object" somewhere, but as far as I am aware, he never did anything with them. It is not, after all, a difficult concept. He certainly never talked about "*-autonomous categories", although Grothendieck (and everyone else who ever gave it a thought) was surely aware that finite dimensional vectors spaces and finite abelian groups were such. If he ever isolated the concept as an interesting one, I am unaware of it and, in any case, I don't believe he ever pursued it (someone would surely have let me know by now). This mad insistence on giving Grothendieck credit for every fleeting idea he may (or even may not) have mentioned somewhere is a perfect example of how the star system (no pun intended) has permeated our consciousness.
I may have misunderstood, but I didn't think anyone even implied that Grothendieck could be credited with *-autonomous categories. Juergen was just asking about the history of the idea of dualizing object, which is just a part of that structure, and certainly predates it. The fact that an idea may have been in the air before it was captured in a structure does not have to decrease the merit of capturing it; on the contrary, it may also be thought of as a sign that it was an important idea, or that capturing it wasn't easy. The fact that Wiles was drawing upon a rich source of ideas does not devaluate his victory.
I am not, of course, blaming Grothendieck for any of this. In another instance, one of the best ideas I ever had has been named after Euler, who never heard of cohomology groups.
This is a remarkable phenomenon, isn't it? Cartesius also knew nothing of Cartesian categories (or squares, or arrows...), and Frobenius could hardly recognize the logical form of his reciprocity... I think Etruscans had this religion, where they systematically attributed all victories to the ancestors, so that the soldiers wouldn't take things too personally. With kind regards, -- Dusko