Re: Bourbaki & category theory

["Fred E.J. Linton" <fejlinton@usa.net>]

Let me add to the remarks on the extent to which Bourbaki did -- or 
did not -- envisage categories or category theory as an appropriate 
vehicle for conveying universal constructs in their expositions of 
other mathematics, by mentioning in this context the late Serge Lang's 
now half-century-old report, originally prepared "for Bourbaki's internal  
consumption", on the cohomology of groups: {Rapport sur la Cohomologie 
des Groupes}, W.A. Benjamin, NY, 1966.

On page 97 of the Benjamin publication, Serge seeks to "definir la
notion de catégorie multilinéaire", notion which his PREFACE indicates
is "due to Cartier" and which figures not only in these 1959-era notes
but also in the first-year graduate algebra course he gave at Columbia 
during the 1958-1959 academic year. (It was my first year at Columbia,
and I remember that course well -- it gave me not only my first exposure
too Serge Lang, and to categories, but to Saul Lubkin and Peter Freyd as
well, each of whom Serge invited to give a "guest lecture" for a day
(it was the era of the "race for the best embedding theorem":-) ).

Whatever else may have been the case then or earlier as regards Bourbaki 
and categories, by 1959 even multilinear categories were being pressed
upon Bourbaki in certain quarters, by certain proponents, without, alas,
much perceptible effect.

Cheers, -- Fred

------ Original Message ------
Received: Thu, 24 May 2012 08:28:11 PM EDT
From: rlk@knighten.org
To: "categories@mta.ca" <categories@mta.ca>
Subject: categories: Re: Bourbaki & category theory



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