Article ID: CBB000770913

La “machine de Grothendieck”, se fonde-t-elle seulement sur des vocables métamathématiques? Bourbaki et les catégories au cours des années cinquante (2006)

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The Bourbaki discussion on category theory in the late 1950s is reconstructed with the help of unpublished sources contained in the French Bourbaki archives and in the late Samuel Eilenberg's Nachlaß, a recently rediscovered collection now in the Columbia University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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Authors & Contributors
Gray, Jeremy
Diestel, Joe
Gario, Paola
Colmez, Pierre
Grothendieck, Alexandre
Serre, Jean Pierre
Journals
Historia Mathematica
Revue d'Histoire des Mathématiques
Historical Records of Australian Science
Llull: Revista de la Sociedad Española de Historia de las Ciencias y de las Técnicas
Archive for History of Exact Sciences
Arabic Sciences and Philosophy
Publishers
Société Mathématique de France
Springer-Verlag
Joseph Henry Press
American Mathematical Society
Birkhäuser
International Press
Concepts
Mathematics
Algebraic geometry
Biographies
Geometry
Algebra
Number theory; number concept
People
Grothendieck, Alexandre
Bourbaki, Nicolas, pseud.
Castelnuovo, Guido
Serre, Jean Pierre
Abel, Niels Henrik
Russell, Bertrand Arthur William
Time Periods
19th century
20th century, early
20th century
20th century, late
9th century
21st century
Places
Italy
France
Australia
Spain
Baghdad (Iraq)
Russia
Institutions
University of Chicago
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