Product preserving bundle functors on fibered fibered manifolds

Włodzimierz M. Mikulski¹ ; Jiří M. Tomáš²

¹ Institute of Mathematics Jagiellonian University Reymonta 4 30-059 Kraków, Poland
² Department of Mathematics Faculty of Chemistry Technical University Brno Purkyňova 118 600 00 Brno, Czech Republic

Colloquium Mathematicum, Tome 96 (2003) no. 1, pp. 17-26.

Résumé

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 ${\cal M}f$ 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.

Détail

DOI : 10.4064/cm96-1-3

Keywords: investigate category product preserving bundle functors defined category fibered fibered manifolds bijective correspondence between category certain category commutative diagrams product preserving bundle functors defined category cal smooth manifolds application theory weil functors latter category considered category commutative diagrams weil algebras mention relation natural transformations between product preserving bundle functors category fibered manifolds