Re: Bourbaki & category theory

["Eduardo J. Dubuc" <edubuc@dm.uba.ar>]

On 22/05/12 14:49, Eduardo J. Dubuc wrote:


> The reason why category theory "is what it is" is that
>
> it is the language that allows to define the notion of universal
> property in its right generality.
>
> The notion of universal property first appears in Bourbaki, which
> decided not to use the language of categories to formulate it, on spite
> of the advice of Grothendieck.
>

Concerning the remark "on spite of the advice of Grothendieck"

(that I concluded following some readings I do not remember where, and 
that if I remember correctly, Grothendieck wanted to rewrite the whole 
project (before it was published) using Category Theory, and presented a 
proposal that after some consideration was turned off by Bourbaki)

I received a private mail that can be of interest to many and that I 
copy and paste below:

===================================================================
Pierre Cartier, Chritian Houzel, Andrej Rodin and Ralf Krömer wrote 
about that issue.

You will find the source material, i.e. the early Bourbaki archives 
(1934-1954), which show various early attempts at defining "structure", 
online at http://mathdoc.emath.fr/archives-bourbaki/
A bibliography of sources on Bourbaki is at 
http://poincare.univ-nancy2.fr/Actu/?contentId=9473

One may not confuse any edition of the first volume of the Elements with 
Bourbaki relatively evolving thoughts on this matter.

There is a lot to be learnt from reading the sources. Please notice that 
I replied to you personally and not to the whole list. Be kind to a shy 
person. Best regards, LB
====================================================================

e.d.


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