Product preserving functors of infinite-dimensional manifolds

Andreas Kriegl; Peter W. Michor

Natural transformations in differential geometry

Gerd Kainz, Peter W. Michor (1987)

Czechoslovak Mathematical Journal

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A convenient setting for differential geometry and global analysis II

Peter Michor (1984)

Cahiers de Topologie et Géométrie Différentielle Catégoriques

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Properties of product preserving functors

Gancarzewicz, Jacek, Mikulski, Włodzimierz, Pogoda, Zdzisław

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A product preserving functor is a covariant functor $ℱ$ 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: $ℱ (M_{1} \times M_{2}) = ℱ (M_{1}) \times ℱ (M_{2})$ . It is known that any product preserving functor $ℱ$ is equivalent to a Weil functor $T^{A}$ . Here $T^{A} (M)$ is the set of equivalence classes of smooth maps $ϕ : ℝ^{n} \to M$ and $ϕ, ϕ^{'}$ are equivalent if and only if for every smooth function $f : M \to ℝ$ the formal Taylor series at 0 of $f \circ ϕ$ and $f \circ ϕ^{'}$ are equal in $A = ℝ [[x_{1}, \dots, x_{n}]] / 𝔞$ . In this...

Displaying similar documents to “Product preserving functors of infinite-dimensional manifolds”

Natural transformations in differential geometry

A convenient setting for differential geometry and global analysis II

Properties of product preserving functors