Bourbaki and foundations

[Robert Black]

This whole thread began with the claim that Grothendieck left Bourbaki
because of the unwillingness of its other members to replace set theory
by category theory as a foundation of mathematics. But just as a piece
of history this can't be true, can it? Grothendieck left Bourbaki in
high dudgeon in the late 1950s. He certainly thought that the first
volume should be rewritten so as to include the basic concepts of
category theory from early on, and that chapter IV, 'Structures' should
be completely replaced treating roughly the same material from a
category-theoretic viewpoint. Today I think everyone would agree with
this, whatever they think about category-theoretic foundations. But he
surely can't have been arguing for *replacing* set theory by category
theory, since in the 1950s nobody, not even Grothendieck, knew how to do
this.

--
Robert Black