Properties of product preserving functors

Gancarzewicz, Jacek, Mikulski, Włodzimierz, and Pogoda, Zdzisław. "Properties of product preserving functors." Proceedings of the Winter School "Geometry and Physics". Palermo: Circolo Matematico di Palermo, 1994. [69]-86. <http://eudml.org/doc/220943>.

@inProceedings{Gancarzewicz1994,
abstract = {A product preserving functor is a covariant functor $\{\mathcal \{F\}\}$ 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: $\{\mathcal \{F\}\} (M_1 \times M_2) = \{\mathcal \{F\}\} (M_1) \times \{\mathcal \{F\}\} (M_2)$. It is known that any product preserving functor $\{\mathcal \{F\}\}$ is equivalent to a Weil functor $T^A$. Here $T^A (M)$ is the set of equivalence classes of smooth maps $\varphi : \mathbb \{R\}^n \rightarrow M$ and $\varphi , \varphi ^\{\prime \}$ are equivalent if and only if for every smooth function $f : M \rightarrow \mathbb \{R\}$ the formal Taylor series at 0 of $f \circ \varphi $ and $f \circ \varphi ^\{\prime \}$ are equal in $A = \mathbb \{R\}[[x_1, \dots , x_n]]/\{\mathfrak \{a\}\}$. In this paper all known properties of product preserving functors are derived from the axioms without using Weil functors.},
author = {Gancarzewicz, Jacek, Mikulski, Włodzimierz, Pogoda, Zdzisław},
booktitle = {Proceedings of the Winter School "Geometry and Physics"},
keywords = {Proceedings; Winter School; Zdíkov (Czech Republic); Geometry; Physics},
location = {Palermo},
pages = {[69]-86},
publisher = {Circolo Matematico di Palermo},
title = {Properties of product preserving functors},
url = {http://eudml.org/doc/220943},
year = {1994},
}

TY - CLSWK
AU - Gancarzewicz, Jacek
AU - Mikulski, Włodzimierz
AU - Pogoda, Zdzisław
TI - Properties of product preserving functors
T2 - Proceedings of the Winter School "Geometry and Physics"
PY - 1994
CY - Palermo
PB - Circolo Matematico di Palermo
SP - [69]
EP - 86
AB - A product preserving functor is a covariant functor ${\mathcal {F}}$ 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: ${\mathcal {F}} (M_1 \times M_2) = {\mathcal {F}} (M_1) \times {\mathcal {F}} (M_2)$. It is known that any product preserving functor ${\mathcal {F}}$ is equivalent to a Weil functor $T^A$. Here $T^A (M)$ is the set of equivalence classes of smooth maps $\varphi : \mathbb {R}^n \rightarrow M$ and $\varphi , \varphi ^{\prime }$ are equivalent if and only if for every smooth function $f : M \rightarrow \mathbb {R}$ the formal Taylor series at 0 of $f \circ \varphi $ and $f \circ \varphi ^{\prime }$ are equal in $A = \mathbb {R}[[x_1, \dots , x_n]]/{\mathfrak {a}}$. In this paper all known properties of product preserving functors are derived from the axioms without using Weil functors.
KW - Proceedings; Winter School; Zdíkov (Czech Republic); Geometry; Physics
UR - http://eudml.org/doc/220943
ER -