The Bourbaki discussion on category theory in the late 1950s is reconstructed with the help of unpublished sources contained in the French Bourbaki archives and in the late Samuel Eilenberg's Nachlaß, a recently rediscovered collection now in the Columbia University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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Alexandre Grothendieck: A Mathematical Portrait
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Parshall, Karen Hunger;
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Episodes in the History of Modern Algebra (1800--1950)
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Diestel, Joe;
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Grothendieck and Banach Space Theory
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Russell et l'Universal Algebra de Whitehead: la géométrie projective entre ordre et incidence (1898--1903)
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Colmez, Pierre;
Serre, Jean Pierre;
(2001)
Correspondance Grothendieck-Serre
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Article
Michael J. Barany;
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Impersonation and personification in mid-twentieth century mathematics
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David Aubin;
Anne-Sandrine Paumier;
(2016)
Polycephalic Euclid? Collective Practices in Bourbaki’s History of Mathematics
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Español González, Luis;
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Avances en la Historia de la Geometría contemporánea española durante el último cuarto de siglo
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Book
Marchisotto, Elena;
Smith, James T.;
(2007)
The Legacy of Mario Pieri in Geometry and Arithmetic
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Agnewa, Alfonso F.;
Bobeb, Alexandru;
Boskoffb, Wladimir G.;
Suceava, Bogdan D.;
(2009)
Gheorghe Titeica and the Origins of Affine Differential Geometry
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Gario, Paola;
(2001)
Guido Castelnuovo: Documents for a Biography
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Article
Alain Herreman;
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Nabonnand, Philippe;
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Wall, G. E.;
Pitman, Jane;
Potts, R. B.;
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Eric Stephen Barnes, 1924--2000
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Paradís, Jaume;
Pla, Josep;
Viader, Pelegrí;
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Fermat's Method of Quadrature
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Sørensen, Henrik Kragh;
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Roshdi Rashed;
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Babbitt, Donald;
Goodstein, Judith R.;
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Guido Castelnuovo and Francesco Severi: Two Personalities, Two Letters
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Book
Derbyshire, John;
(2006)
Unknown Quantity: A Real and Imaginary History of Algebra
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