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.

UDC: 514.16

Received: 17.12.2004