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 [For admin and other information see: http://www.mta.ca/~cat-dist/ ]