Previous |  Up |  Next


product preserving functors; convenient vector spaces; $C^\infty$-algebras
The theory of product preserving functors and Weil functors is partly extended to infinite dimensional manifolds, using the theory of $C^\infty $-algebras.
[1] Eck, D. J.: Product preserving functors on smooth manifolds. J. Pure and Applied Algebra 42 (1986), 133–140. MR 0857563 | Zbl 0615.57019
[2] Frölicher, A., Kriegl, A.: Linear spaces and differentiation theory. Pure and Applied Mathematics, J. Wiley, Chichester, 1988. MR 0961256
[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 0894394
[4] Kainz, G., Michor, P. W.: Natural transformations in differential geometry. Czechoslovak Math. J. 37 (1987), 584-607. MR 0913992
[5] Kolář, I.: Covariant approach to natural transformations of Weil functors. Comment. Math. Univ. Carolin. 27 (1986), 723–729. MR 0874666
[6] Kolář, I.,; Michor, P. W., Slovák, J.: Natural operations in differential geometry. Springer-Verlag, Berlin, Heidelberg, New York, 1993, pp. vi+434. MR 1202431
[7] Kriegl, A., Michor, P. W.: A convenient setting for real analytic mappings. Acta Mathematica 165 (1990), 105–159. MR 1064579
[8] Kriegl, A., Michor, P. W.: Aspects of the theory of infinite dimensional manifolds. Differential Geometry and Applications 1 (1991), 159–176. MR 1244442
[9] Kriegl, A., Michor, P. W.: Regular infinite dimensional Lie groups. to appear, J. Lie Theory (1997). MR 1450745
[10] Kriegl, A., Michor, P. W.: The Convenient Setting for Global Analysis. to appear, Surveys and Monographs, AMS, Providence, 1997. MR 1471480
[11] Kriegl, A., Nel, L. D.: A convenient setting for holomorphy. Cahiers Top. Géo. Diff. 26 (1985), 273–309. MR 0796352
[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 0552656 | Zbl 0403.18005
[13] Luciano, O. O.: Categories of multiplicative functors and Weil’s infinitely near points. Nagoya Math. J. 109 (1988), 69–89. MR 0931952 | Zbl 0661.58007
[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 0830252 | Zbl 0594.22009
[16] Moerdijk, I., Reyes G. E.: Models for smooth infinitesimal analysis. Springer-Verlag, Heidelberg Berlin, 1991. MR 1083355
[17] Moerdijk, I., Reyes G. E.: Rings of smooth funcions and their localizations, I. J. Algebra 99 (1986), 324–336. MR 0837547
[18] Morimoto, A.: Prolongations of connections to bundles of infinitely near points. J. Diff. Geom. 11 (1976), 479–498. MR 0445422
[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 0930685
[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 0688131
[21] Weil, A.: Théorie des points proches sur les variétés differentielles. Colloque de topologie et géométrie différentielle, Strasbourg, 1953, pp. 111–117. MR 0061455
Partner of
EuDML logo