Displaying similar documents to “On the geometric functors on manifolds”

Fiber product preserving bundle functors on all morphisms of fibered manifolds

Ivan Kolář, Włodzimierz M. Mikulski (2006)

Archivum Mathematicum

Similarity:

We describe the fiber product preserving bundle functors on the category of all morphisms of fibered manifolds in terms of infinite sequences of Weil algebras and actions of the skeleton of the category of r -jets by algebra homomorphisms. We deduce an explicit formula for the iteration of two such functors. We characterize the functors with values in vector bundles.

Natural transformations of Weil functors into bundle functors

Mikulski, Włodzimierz M.

Similarity:

[For the entire collection see Zbl 0699.00032.] Natural transformations of the Weil functor T A of A-velocities [, Commentat. Math. Univ. Carol. 27, 723-729 (1986; Zbl 0603.58001)] into an arbitrary bundle functor F are characterized. In the case where F is a linear bundle functor, the author deduces that the dimension of the vector space of all natural transformations of T A into F is finite and is less than or equal to dim ( F 0 ℛ k ) . The spaces of all natural transformations of Weil functors into...