bourbaki_and_disdain

[edubuc <edubuc@dm.uba.ar>]

Hello

1) I agree completely with Andre, or, more properly, with Samuel
Eilemberg and Pierre Cartier (Andre just tel us what they said to him
when he ask them the question)

So the problem is not wether to agree with Andre or not, but wether to
agree with Eilemberg-Cartier or not. They said to Andre:

"Bourbaki had essentially two options: rewrite the whole treaty using
categories,
or just introduce them in the book on homological algebra,
The second option won, essentially because of the enormity of the task
of rewriting everything."

2) We can see that this makes sense too, the  Bourbaki Tractate was
already written, and Grothendieck's proposal was to entirely rewrite the
thing !!

3) Also, Bourbaki Tractate, as it is, is a masterful book. It is just
perfect, or as close to perfection as possible. It sets a way,
philosophy and style to write mathematics. I myself (as Andre) have
learned a lot by reading Bourbaki, and, more than that, I enjoyed the
reading (and the task to understand it) as much as I enjoy any reading
where I can see perfection in every sense (as in Borges for example).

4) So, it is a lost  for mathematics and for category theory that
category theory fit in Bourbaki's goal as a foundational theory (as set
theory is) , and not just as one more part of mathematics (as set theory
is not).

What a marvelous book just on category theory Bourbaki could have
written, can you imagine !!

A Boubaki book on category theory !!

We miss it  . . .

5) Concerning "desdain", I recall to all of you that most of the people
who show desdain for category theory, also show desdain for Bourbaki.

Eduardo.