Geodesic
Weil functors for the category of manifolds depending on parameters
Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 37-49 Cet article a éte moissonné depuis la source Math-Net.Ru

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A Weil functor $T^\mathbb A:\mathcal Mf\to\mathcal{FM}$ defined of local Weil algebra $\mathbb A$ assigns to an object $M\times\mathbb R^N\to\mathbb R^N$ of the category $\mathcal Mf^N$ of manifolds depending on $N$ parameters the fibration $T^\mathbb A(M\times\mathbb R^N)\to T^\mathbb A\mathbb R^N$. In this article we show that any cross-section $\mathbb R^N\to T^\mathbb A\mathbb R^N$ induces the product preserving functor on the category $\mathcal Mf^N$. We obtain condition of the equivalence for these functors. 
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G. N. Bushueva. Weil functors for the category of manifolds depending on parameters. Učënye zapiski Kazanskogo universiteta. Seriâ Fiziko-matematičeskie nauki, Труды геометрического семинара, Tome 147 (2005) no. 1, pp. 37-49. http://geodesic.mathdoc.fr/item/UZKU_2005_147_1_a4/

[1] Weil A., “Théorie des points proches sur les variététes différentiables”, Colloque Int. Centre Nat. Rech. Sci., 52, Strasbourg, 1953, 111–117 | MR | Zbl

[2] Kolář I., Michor P., Slovák J., Natural operations in differential geometry, Springer-Verlag, Berlin–Heidelberg, 1993, 434 pp. | MR

[3] Shurygin V. V., “Gladkie mnogoobraziya nad lokalnymi algebrami i rassloeniya Veilya”, Itogi nauki i tekhniki. Sovremennaya matem. i ee prilozh., 73, Tematicheskie obzory, VINITI, M., 2002, 162–236 | Zbl

[4] Shurygin V. V., “The structure of smooth mappings over Weil algebras and the category of manifolds over algebras”, Lobachevskii J. of Math., 5 (1999), 29–55 ; URL: http://www.ljm.ksu.ru | MR | Zbl

[5] Vagner V. V., “Algebraicheskaya teoriya kasatelnykh prostranstv vysshikh poryadkov”, Tr. sem. po vekt. i tenz. anal., 10, MGU, 1956, 31–88 | MR

[6] Shirokov A. P., “Geometriya kasatelnykh rassloenii i prostranstva nad algebrami”, Itogi nauki i tekhniki. Problemy geometrii, 12, VINITI, M., 1981, 61–95 | MR

[7] Sultanov A. Ya., “Prodolzheniya tenzornykh polei i svyaznostei na rassloeniya Veilya”, Izv. vuzov. Matematika, 1999, no. 9, 81–90 | MR

[8] Morimoto A., “Prolongation of connections to bundles of infinitely near points”, J. Diff. Geom., 11:4 (1976), 479–498 | MR | Zbl

[9] Patterson L.-N., “Connexions and prolongations”, Canad. J. Math., 27:4 (1975), 766–791 | DOI | MR | Zbl

[10] Yuen P. C., “Sur la notion d'une $G$-structure déométrique et les $A$-prolongements de $G$-structures”, C. R. Acad. Sci., 270:24 (1970), A1589–A1592

[11] Bushueva G. N., Dvizheniya v obobschennykh prostranstvakh, Penza, 2002, 24–34

[12] Kolář I., Mikulski W. M., “On the fiber product preserving bundle functors”, Differ. Geom. and Appl., 11 (1999), 105–115 | DOI | MR | Zbl

[13] Mikulski W. M., “Product preserving bundle functors on fibered manifolds”, Archiv. Math., 32 (1996), 307–316 | MR | Zbl

[14] Doupovec M., Kolář I., “Iteration of fiber product preserving bundle functors”, Monatsh. Math., 134 (2001), 39–50 | DOI | MR | Zbl

[15] Doupovec M., Kolář I., “Natural affinors on time-dependent Weil bundles”, Arch. Math., 27 (1991), 205–209 | MR

[16] Leng S., Algebra, Mir, M., 1968, 564 pp.

[17] Feis K., Algebra: koltsa, moduli i kategorii, v. 1, Mir, M., 1977, 688 pp.

[18] Pommare Zh., Sistemy uravnenii s chastnymi proizvodnymi i psevdogruppy Li, Mir, M., 1983, 400 pp. | MR | Zbl