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Model and Mathematics: From the 19th to the 21st CenturyThe Dialectics Archetypes/Types (Universal Categorical Constructions/Concrete Models) in the Work of Alexander Grothendieck

Model and Mathematics: From the 19th to the 21st Century: The Dialectics Archetypes/Types... [We present two basic directions that Grothendieck explores in the transit between archetypes (universal categorical constructions) and types (concrete models): (1) projecting archetypes to types in the 1950s (around the Tôhoku and Riemann-Roch), (2) embedding types into archetypes in the 1980s (around Pursuing Stacks and Dérivateurs). We also discuss (3) his general remarks about “models” in Récoltes et semailles.] http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png

Model and Mathematics: From the 19th to the 21st CenturyThe Dialectics Archetypes/Types (Universal Categorical Constructions/Concrete Models) in the Work of Alexander Grothendieck

Part of the Trends in the History of Science Book Series
Editors: Friedman, Michael; Krauthausen, Karin
Zalamea, Fernando
Model and Mathematics: From the 19th to the 21st Century — Aug 9, 2022
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Publisher
Springer International Publishing
Copyright
© The Editor(s) (if applicable) and The Author(s) 2022. This an Open Access book.
ISBN
978-3-030-97832-7
Pages
267 –275
DOI
10.1007/978-3-030-97833-4_8
Publisher site
See Chapter on Publisher Site

Abstract

[We present two basic directions that Grothendieck explores in the transit between archetypes (universal categorical constructions) and types (concrete models): (1) projecting archetypes to types in the 1950s (around the Tôhoku and Riemann-Roch), (2) embedding types into archetypes in the 1980s (around Pursuing Stacks and Dérivateurs). We also discuss (3) his general remarks about “models” in Récoltes et semailles.]

Published: Aug 9, 2022

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