Re: Bourbaki and Categories

["zoran skoda" <zskoda@gmail.com>]

>
> sustainable in commutative algebra anymore, and the discord between
> Grothendieck and Bourbaki may well have been rooted in this rejection.


I can not recall where, but I read more than once more detailed descriptions
on
what Bourbaki did not accept from Grothendieck. The conservativeness
of Bourbaki who did not accept the usage of category theory (not only
"neglect")
and non-acceptance of a very general approach of Grothendieck to the
notion of "manifold" he envisioned for the future Bourbaki works
were some of the
main points of departure. The remark that as a proponent of "structures"
Bourbaki
had to include categories is anyway a bit lacking an argument. First of all,
because
of the size problems one can not take big categories on equal footing with,
say groups,
and considering only small categories would be strange and lacking most
interesting
examples. On the other hand, Grothendieck judged the lack stemming in
conservativeness
rather than in consistency of the structure-oriented style. Indeed,
according to Dieudonne,
Bourbaki felt comfortable only in including to the books already
(meta)stable, "dead" mathematics
and not the structures in the unstable "living" phase of development.
This was the intended scope and self-conscious (according to Dieudonne)
limitation of the work.
One can accept this and still cry for an exception for so economic tool
as the category theory (if taken in conservative and very basic sense),
especially
in the vision of the wish for generality, Bourbaki followed otherwise.

Zoran Skoda