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Properties of product preserving functors

Gancarzewicz, JacekMikulski, WłodzimierzPogoda, Zdzisław — 1994

Proceedings of the Winter School "Geometry and Physics"

A product preserving functor is a covariant functor from the category of all manifolds and smooth mappings into the category of fibered manifolds satisfying a list of axioms the main of which is product preserving: ( M 1 × M 2 ) = ( M 1 ) × ( M 2 ) . It is known that any product preserving functor is equivalent to a Weil functor T A . Here T A ( M ) is the set of equivalence classes of smooth maps ϕ : n M and ϕ , ϕ ' are equivalent if and only if for every smooth function f : M the formal Taylor series at 0 of f ϕ and f ϕ ' are equal in A = [ [ x 1 , , x n ] ] / 𝔞 . In this paper all...

Liftings of functions and vector fields to natural bundles

CONTENTS0. Introduction...................................................................................................51. Natural bundles...........................................................................................102. Liftings of functions.....................................................................................153. Liftings of functions to the r-frame bundle...................................................224. A space of liftings of functions.....................................................................265....

Connections of higher order and product preserving functors

Jacek GancarzewiczNoureddine RahmaniModesto R. Salgado — 2002

Czechoslovak Mathematical Journal

In this paper we consider a product preserving functor of order r and a connection Γ of order r on a manifold M . We introduce horizontal lifts of tensor fields and linear connections from M to ( M ) with respect to Γ . Our definitions and results generalize the particular cases of the tangent bundle and the tangent bundle of higher order.

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