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Categories of multiplicative functors and Weil’s infinitely near points

Published online by Cambridge University Press:  22 January 2016

O. O. Luciano
O. O. Luciano*
Affiliation:
Instituto de Matematica e Estatistica, Universidade de Sao Paulo, Caixa Postal 20. 570 (Agencia Iguatemi), 01498—SAO PAULO, Brasil and Institut Fourier, Université de Grenoble I, Laboratoire de Mathématiques, B.P. 74, 38402 St-Martin-d’Hères, France
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At the early fifties A. Weil introduced [3] and algebraic approach to the theory of infinitesimal prolongations of smooth manifolds motivated by the theory of jets developed by Ch. Ehresmann on one side and also by the return to Fermat’s methods on the infinitesimal calculus of first order, that makes use of nilpotent infinitesimals.

Type
Research Article
Information
Nagoya Mathematical Journal , Volume 109 , March 1988 , pp. 69 - 89
Copyright
Copyright © Editorial Board of Nagoya Mathematical Journal 1988

References

[1] Kainz, G. and Michor, P., Natural transformations in differential geometry, to appear in Czech. Math. J.Google Scholar
[1] Luciano, Odilon Otavio, Nébuleuses infinitésimalement fibrées, Works of the Dept. of Math., 85, Univ. of Sao Paulo, 1985.Google Scholar
[1] Morimoto, A., Prolongations of geometric structures, Math. Inst. Nagoya University, Chikusa-Ku, Nagoya, Japan, 1969.Google Scholar
[1] Weil, A., Théorie des points proches sur les variétés différentielles, Colloque de Topologie et Géométrie Différentielle, Strasbourg, 1953, 111–117.Google Scholar