Fiber product preserving bundle functors as modified vertical Weil functors

Włodzimierz M. Mikulski

Czechoslovak Mathematical Journal (2015)

  • Volume: 65, Issue: 2, page 517-528
  • ISSN: 0011-4642

Abstract

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We introduce the concept of modified vertical Weil functors on the category ℱ ℳ m of fibred manifolds with m -dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on ℱ ℳ m in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors T A corresponding to Weil algebras A by the so called modified Weil functors T A corresponding to Weil algebra bundle functors A on the category ℳ m of m -dimensional manifolds and their embeddings.

How to cite

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Mikulski, Włodzimierz M.. "Fiber product preserving bundle functors as modified vertical Weil functors." Czechoslovak Mathematical Journal 65.2 (2015): 517-528. <http://eudml.org/doc/270135>.

@article{Mikulski2015,
abstract = {We introduce the concept of modified vertical Weil functors on the category $\mathcal \{F\}\mathcal \{M\}_m$ of fibred manifolds with $m$-dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on $\mathcal \{F\}\mathcal \{M\}_m$ in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors $T^A$ corresponding to Weil algebras $A$ by the so called modified Weil functors $T^A$ corresponding to Weil algebra bundle functors $A$ on the category $\mathcal \{M\}_m$ of $m$-dimensional manifolds and their embeddings.},
author = {Mikulski, Włodzimierz M.},
journal = {Czechoslovak Mathematical Journal},
keywords = {Weil algebra; Weil functor; vertical Weil functor; Weil algebra bundle functor; modified Weil functor; modified vertical Weil functor; bundle functor; fiber product preserving bundle functor; natural transformation},
language = {eng},
number = {2},
pages = {517-528},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Fiber product preserving bundle functors as modified vertical Weil functors},
url = {http://eudml.org/doc/270135},
volume = {65},
year = {2015},
}

TY - JOUR
AU - Mikulski, Włodzimierz M.
TI - Fiber product preserving bundle functors as modified vertical Weil functors
JO - Czechoslovak Mathematical Journal
PY - 2015
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 65
IS - 2
SP - 517
EP - 528
AB - We introduce the concept of modified vertical Weil functors on the category $\mathcal {F}\mathcal {M}_m$ of fibred manifolds with $m$-dimensional bases and their fibred maps with embeddings as base maps. Then we describe all fiber product preserving bundle functors on $\mathcal {F}\mathcal {M}_m$ in terms of modified vertical Weil functors. The construction of modified vertical Weil functors is an (almost direct) generalization of the usual vertical Weil functor. Namely, in the construction of the usual vertical Weil functors, we replace the usual Weil functors $T^A$ corresponding to Weil algebras $A$ by the so called modified Weil functors $T^A$ corresponding to Weil algebra bundle functors $A$ on the category $\mathcal {M}_m$ of $m$-dimensional manifolds and their embeddings.
LA - eng
KW - Weil algebra; Weil functor; vertical Weil functor; Weil algebra bundle functor; modified Weil functor; modified vertical Weil functor; bundle functor; fiber product preserving bundle functor; natural transformation
UR - http://eudml.org/doc/270135
ER -

References

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  8. Luciano, O. O., 10.1017/S0027763000002774, Nagoya Math. J. 109 (1988), 69-89. (1988) Zbl0661.58007MR0931952DOI10.1017/S0027763000002774
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