La “machine de Grothendieck”, se fonde-t-elle seulement sur des vocables métamathématiques? Bourbaki et les catégories au cours des années cinquante (2006)
The Bourbaki discussion on category theory in the late 1950s is reconstructed with the help of unpublished sources contained in the French Bourbaki archives and in the late Samuel Eilenberg's Nachlaß, a recently rediscovered collection now in the Columbia University archives. Special attention is given to the relation between this discussion and Grothendieck's participation in the Bourbaki project. Grothendieck's work on homological algebra and algebraic geometry was the major motivation for attempts to adopt categories in Bourbaki's Eléments; but this adoption failed for several reasons, including a conflict of Bourbaki's concept of structure with categories, but also the problems to give set theoretical foundations for category theory (which eventually led Grothendieck to introduce the notion of Universe which bears nowadays his name) and André Weil's personal disapproval. It is shown that Bourbaki's refusal to adopt category theory was among the reasons which led Grothendieck to leave the group.
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