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Keywords:
Weil functor; natural transformation of Weil bundles
Weil functor; natural transformation of Weil bundles
Summary:
First we deduce some general results on the covariant form of the natural transformations of Weil functors. Then we discuss several geometric properties of these transformations, special attention being paid to vector bundles and principal bundles.
References:
[1] Ehresmann, C.: Oeuvres complètes et commentés, Parties I–1 et I–2. Cahiers Topol. Géom. Diff. XXIV (Suppl. 1 et 2) (1983).
[2] Kolář, I.: Affine structures on Weil bundles. Nagoya Math. J. 158 (2000), 99–106.
[3] Kolář, I.: Handbook of Global Analysis. ch. Weil Bundles as Generalized Jet Spaces, pp. 625–664, Elsevier, Amsterdam, 2008. MR 2389643
[4] Kolář, I.: On the functorial prolongations of fiber bundles. Proceedings of AGMP 8, 2012.
[5] Kolář, I., Michor, P. W., Slovák, J.: Natural Operations in Differential Geometry. Springer Verlag, 1993.
[6] Weil, A.: Théorie des points proches sur les variétées différentiables. Colloques internat. Centre nat. Rech. Sci. 52 (1953), 111–117.
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