We investigate the category of product preserving bundle functors defined on the category of fibered fibered manifolds. We show a bijective correspondence between this category and a certain category of commutative diagrams on product preserving bundle functors defined on the category ℳ f of smooth manifolds. By an application of the theory of Weil functors, the latter category is considered as a category of commutative diagrams on Weil algebras. We also mention the relation with natural transformations between product preserving bundle functors on the category of fibered manifolds.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-3,
author = {W\l odzimierz M. Mikulski and Ji\v r\'\i\ M. Tom\'a\v s},
title = {Product preserving bundle functors on fibered fibered manifolds},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {17-26},
zbl = {1045.58001},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-3}
}
Włodzimierz M. Mikulski; Jiří M. Tomáš. Product preserving bundle functors on fibered fibered manifolds. Colloquium Mathematicae, Tome 96 (2003) pp. 17-26. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-3/