Product preserving functors of infinite-dimensional manifolds
Archivum mathematicum, Tome 32 (1996) no. 4, pp. 289-306 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of $C^\infty $-algebras.
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of $C^\infty $-algebras.
Classification : 58B99
Keywords: product preserving functors; convenient vector spaces; $C^\infty$-algebras
@article{ARM_1996_32_4_a4,
     author = {Kriegl, Andreas and Michor, Peter W.},
     title = {Product preserving functors of infinite-dimensional manifolds},
     journal = {Archivum mathematicum},
     pages = {289--306},
     year = {1996},
     volume = {32},
     number = {4},
     mrnumber = {1441400},
     zbl = {0881.58010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a4/}
}
TY  - JOUR
AU  - Kriegl, Andreas
AU  - Michor, Peter W.
TI  - Product preserving functors of infinite-dimensional manifolds
JO  - Archivum mathematicum
PY  - 1996
SP  - 289
EP  - 306
VL  - 32
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a4/
LA  - en
ID  - ARM_1996_32_4_a4
ER  - 
%0 Journal Article
%A Kriegl, Andreas
%A Michor, Peter W.
%T Product preserving functors of infinite-dimensional manifolds
%J Archivum mathematicum
%D 1996
%P 289-306
%V 32
%N 4
%U http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a4/
%G en
%F ARM_1996_32_4_a4
Kriegl, Andreas; Michor, Peter W. Product preserving functors of infinite-dimensional manifolds. Archivum mathematicum, Tome 32 (1996) no. 4, pp. 289-306. http://geodesic.mathdoc.fr/item/ARM_1996_32_4_a4/

[1] Eck, D. J.: Product preserving functors on smooth manifolds. J. Pure and Applied Algebra 42 (1986), 133–140. | MR | Zbl

[2] Frölicher, A., Kriegl, A.: Linear spaces and differentiation theory. Pure and Applied Mathematics, J. Wiley, Chichester, 1988. | MR

[3] Kainz, G., Kriegl, A., Michor, P. W.: $C^\infty $-algebras from the functional analytic viewpoint. J. pure appl. Algebra 46 (1987), 89-107. | MR

[4] Kainz, G., Michor, P. W.: Natural transformations in differential geometry. Czechoslovak Math. J. 37 (1987), 584-607. | MR

[5] Kolář, I.: Covariant approach to natural transformations of Weil functors. Comment. Math. Univ. Carolin. 27 (1986), 723–729. | MR

[6] Kolář, I.,; Michor, P. W., Slovák, J.: Natural operations in differential geometry. Springer-Verlag, Berlin, Heidelberg, New York, 1993, pp. vi+434. | MR

[7] Kriegl, A., Michor, P. W.: A convenient setting for real analytic mappings. Acta Mathematica 165 (1990), 105–159. | MR

[8] Kriegl, A., Michor, P. W.: Aspects of the theory of infinite dimensional manifolds. Differential Geometry and Applications 1 (1991), 159–176. | MR

[9] Kriegl, A., Michor, P. W.: Regular infinite dimensional Lie groups. to appear, J. Lie Theory (1997). | MR

[10] Kriegl, A., Michor, P. W.: The Convenient Setting for Global Analysis. to appear, Surveys and Monographs, AMS, Providence, 1997. | MR

[11] Kriegl, A., Nel, L. D.: A convenient setting for holomorphy. Cahiers Top. Géo. Diff. 26 (1985), 273–309. | MR

[12] Lawvere, F. W.: Categorical dynamics. Lectures given 1967 at the University of Chicago, reprinted in, Topos Theoretical Methods in Geometry, A. Kock (ed.), Aarhus Math. Inst. Var. Publ. Series 30, Aarhus Universitet, 1979. | MR | Zbl

[13] Luciano, O. O.: Categories of multiplicative functors and Weil’s infinitely near points. Nagoya Math. J. 109 (1988), 69–89. | MR | Zbl

[14] Michor, P. W., Vanžura, J.: Characterizing algebras of smooth functions on manifolds. to appear, Comm. Math. Univ. Carolinae (Prague).

[15] Milnor, J.: Remarks on infinite dimensional Lie groups. Relativity, Groups, and Topology II, Les Houches, 1983, B.S. DeWitt, R. Stora, Eds., Elsevier, Amsterdam, 1984. | MR | Zbl

[16] Moerdijk, I., Reyes G. E.: Models for smooth infinitesimal analysis. Springer-Verlag, Heidelberg Berlin, 1991. | MR

[17] Moerdijk, I., Reyes G. E.: Rings of smooth funcions and their localizations, I. J. Algebra 99 (1986), 324–336. | MR

[18] Morimoto, A.: Prolongations of connections to bundles of infinitely near points. J. Diff. Geom. 11 (1976), 479–498. | MR

[19] Moerdijk, I., Ngo Van Que, Reyes G. E.: Rings of smooth funcions and their localizations, II. Mathematical logic and theoretical computer science, D.W. Kueker, E.G.K. Lopez-Escobar, C.H. Smith (eds.), Marcel Dekker, New York, Basel, 1987. | MR

[20] Omori, H., Maeda, Y., Yoshioka, A.: On regular Fréchet Lie groups IV. Definitions and fundamental theorems. Tokyo J. Math. 5 (1982), 365–398. | MR

[21] Weil, A.: Théorie des points proches sur les variétés differentielles. Colloque de topologie et géométrie différentielle, Strasbourg, 1953, pp. 111–117. | MR