Re: Juergen's question

[Dusko Pavlovic <dusko@kestrel.edu>]

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