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Daniel Quillen, the father of abstract homotopy theory

Published online by Cambridge University Press:  01 March 2013

Jean-Claude Thomas  and
Micheline Vigué-Poirrier
Jean-Claude Thomas
Affiliation:
LAREMA, UMR CNRS 6093, Université d'Angers, 2, Boulevard Lavoisier, 49045 Angers, Francejean-claude.thomas@univ-angers.fr
Micheline Vigué-Poirrier
Affiliation:
LAGA, UMR CNRS 7539, Université de Paris 13, Institut Galilée, 93430 Villetaneuse, Francevigue@math.univ-paris13.fr
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Abstract

In this short paper we try to describe the fundamental contribution of Quillen in the development of abstract homotopy theory and we explain how he uses this theory to lay the foundations of rational homotopy theory.

Keywords

Model categoryQuillen functorsHomotopical algebraRational homotopy type55-0155P6255P65

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Type
Research Article
Information
Journal of K-Theory , Volume 11 , Issue 3: The Legacy of Daniel Quillen , June 2013 , pp. 479 - 491
Copyright
Copyright © ISOPP 2013 

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