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: $ℱ(M_1\times M_2)=ℱ\left(M_1\right)\times ℱ\left(M_2\right)$. It is known that any product preserving functor $ℱ$ is equivalent to a Weil functor $T^A$. Here $T^A\left(M\right)$ is the set of equivalence classes of smooth maps $\varphi :{ℝ}^n\to M$ and $\varphi ,{\varphi }^{\text{'}}$ are equivalent if and only if for every smooth function $f:M\to ℝ$ the formal Taylor series at 0 of $f\circ \varphi$ and $f\circ {\varphi }^{\text{'}}$ are equal in $A=ℝ\left[[x_1,\cdots ,x_n]\right]/𝔞$. In this paper all known properties of product preserving functors are derived from the axioms without using Weil functors.

EUDML-ID : urn:eudml:doc:220943
Mots clés:

@article{701546,
     title = {Properties of product preserving functors},
     booktitle = {Proceedings of the Winter School "Geometry and Physics"},
     series = {GDML\_Books},
     publisher = {Circolo Matematico di Palermo},
     address = {Palermo},
     year = {1994},
     pages = {[69]-86},
     mrnumber = {MR1344002},
     zbl = {0848.55010},
     url = {http://dml.mathdoc.fr/item/701546}
}

Gancarzewicz, Jacek; Mikulski, Włodzimierz; Pogoda, Zdzisław. Properties of product preserving functors, dans Proceedings of the Winter School "Geometry and Physics", GDML_Books,  (1994), pp. [69]-86. http://gdmltest.u-ga.fr/item/701546/