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The title is a quote of either Pierre Cartier or Jean Benabou in a public discussion at the ENS. Cartier and Benabou agreed about it on stage, at the time, and later said I could cite them though neither recalled who first said it. But a quote of Barry Mazur reminds us that Grothendieck believed somehow in every concept he explored. We can see the resolution in Grothendieck’s 33 hours of tape-recorded lectures and workshops in Buffalo NY in June and July 1973: Where he considered the concepts of topos and scheme perfectly adapted to the goal, he considered universes a valuable technical tool not yet in final form. In Buffalo he described their role, and a possible improvement suggested by Pierre Samuel which is related to a device recently used by Peter Scholz.

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Grothendieck Did Not Believe in Universes, He Believed in Topos and Schemes

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  • 发表日期：

    2025年

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  • Colin McLarty

摘要

The title is a quote of either Pierre Cartier or Jean Benabou in a public discussion at the ENS. Cartier and Benabou agreed about it on stage, at the time, and later said I could cite them though neither recalled who first said it. But a quote of Barry Mazur reminds us that Grothendieck believed somehow in every concept he explored. We can see the resolution in Grothendieck’s 33 hours of tape-recorded lectures and workshops in Buffalo NY in June and July 1973: Where he considered the concepts of topos and scheme perfectly adapted to the goal, he considered universes a valuable technical tool not yet in final form. In Buffalo he described their role, and a possible improvement suggested by Pierre Samuel which is related to a device recently used by Peter Scholz.