Bourbaki and Categories

[Walter Tholen <tholen@mathstat.yorku.ca>]

Here is some up-lifting press about categories that I saw in an article
by Karl  Heinrich Hofmann entitled "Bourbaki in T"ubingen und in den
USA, Erinnerungen an die franz"osische Revolution in der Mathematik",
which may translate as "Bourbaki in Tubingen and in the USA,
reminiscenses of the French revolution in mathematics", and which
appeared in the "Mitteilungen der DMV" (the German equivalent of the AMS
Notices, which is distributed to all members), vol 16.2 (2008),
pp128-136. While the author has a lot of praise for Bourbaki's work, he
lists also a number of "defects of the Bourbaki concept", and the
following appears quite prominently in his article (my translation,
okayed by the author):

"Since Bourbaki is considered as the exponent of the theory of
mathematical structures, it is truly surprising that the theory of
categories (S. Eilenberg and S. Mac Lane, 1946) was almost demonstrably
ignored as the mother of all structure theories. This was hardly
sustainable in commutative algebra anymore, and the discord between
Grothendieck and Bourbaki may well have been rooted in this rejection.
This dismissive position is even more surprising since Eilenberg as one
of the few non-French people belonged to the early Bourbaki group, and
since the French founder of category theory, Charles Ehresmann, was at
times closely connected with Bourbaki. In my view this failure of
Bourbaki is grave."