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Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 2005, Volume 147, Book 1, Pages 37–49 (Mi uzku478)  

Weil functors for the category of manifolds depending on parameters

G. N. Bushueva

N. G. Chebotarev Research Institute of Mathematics and Mechanics, Kazan State University

Abstract: 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.

Full text: PDF file (286 kB)
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UDC: 514.16
Received: 17.12.2004

Citation: G. N. Bushueva, “Weil functors for the category of manifolds depending on parameters”, Труды геометрического семинара, Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki, 147, no. 1, Kazan University, Kazan, 2005, 37–49

Citation in format AMSBIB
\Bibitem{Bus05}
\by G.~N.~Bushueva
\paper Weil functors for the category of manifolds depending on parameters
\inbook Труды геометрического семинара
\serial Kazan. Gos. Univ. Uchen. Zap. Ser. Fiz.-Mat. Nauki
\yr 2005
\vol 147
\issue 1
\pages 37--49
\publ Kazan University
\publaddr Kazan
\mathnet{http://mi.mathnet.ru/uzku478}


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