Re: Bourbaki and Categories

[Colin McLarty <colin.mclarty@case.edu>]

From: zoran skoda <zskoda@gmail.com>
Date: Friday, September 12, 2008 2:06 pm

wrote, among other things

> 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.

The claim is not that Bourbaki should have studied categories as
structures.  It is that Bourbaki was doomed to fail in trying to use
their structure theory.  Leo Corry shows in his book "Modern Algebra and
the Rise of Mathematical Structures" (Birkhäuser 1996) that they did fail.  

And they should have seen this coming, because their theory had been 

"superseded by that of category and functor, which includes it under a
more general
and convenient form" (Dieudonné "The Work of Nicholas Bourbaki" 1970).

best, Colin