Bourbaki and Categories

[John Baez <baez@math.ucr.edu>]

On Fri, Sep 19, 2008 at 10:16:31PM -0400, jim stasheff wrote:

> John Baez wrote:

> >I can imagine a new Bourbaki who tries to explain all of
> >mathematics in the language of categories.  But I can
> >also imagine a new Bourbaki who tries to explain all of
> >mathematics in the language of infinity-categories.

> Is it necessary to have a global point of view to appreciate Bourbaki? I
> found them quite valuable locally - i.e.. just a few of the chapters by
> themselves earned my appreciation.

It's easy to appreciate their books locally - but I think they
sought a global systematic viewpoint while writing them.

It's possible that a "neo-Bourbaki" should take a less systematic
approach.  Mathematics may be too much in a state of foundational
flux for a systematic approach to be successful right now.  Maybe
the best we can hope for is something a bit more like Wikipedia,
where different people contribute different portions of text, and
they don't cohere in a polished whole.  But presumably anyone calling
for a new Bourbaki wants something different from Wikipedia.

There's "Scholarpedia":

http://www.scholarpedia.org/

but it doesn't seem to be doing anything with math yet, and if
it ever does, I bet it'll take a "midde-of-the-road" approach instead
of pushing a specific intellectual agenda.

I would like to see lots of people try lots of different things.

Best,
jb