Publication detail

Vertical functors on fibered manifolds

DOUPOVEC, M. KUREK, J. MIKULSKI, W.

Original Title

Vertical functors on fibered manifolds

Type

journal article in Web of Science

Language

English

Original Abstract

The usual vertical functor V on all fibered manifold morphisms is a classical example of a fiber product preserving bundle functor. In the present paper we extend almost directly the concept of the vertical functor V to the ones of modified or generalized vertical Weil functors and using them we describe completely the fiber product preserving bundle functors on many categories of fibered manifolds. More precisely, we fix an admissible category C over manifolds and let FMC be the category of fibered manifolds with bases being C-objects and their fibered maps with base maps being C-morphisms. We introduce the concept of modified vertical Weil functor on FMC and prove that any finite order fiber product preserving regular bundle functor on FMC is isomorphic to a modified vertical Weil functor. We also study finite order regular fiber product preserving bundle functors of vertical type and describe these functors by generalized vertical Weil functors. Finally we study the iteration of finite order regular fiber product preserving bundle functors on FMC. © 2017 Elsevier B.V. All rights reserved.

Keywords

Weil algebra bundle functor Modified Weil functor Modified vertical Weil functor Fiber product preserving bundle functor

Authors

DOUPOVEC, M.; KUREK, J.; MIKULSKI, W.

Released

1. 9. 2017

Publisher

ELSEVIER

Location

Nizozemsko

ISBN

0926-2245

Periodical

DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS

Year of study

54

Number

A

State

Kingdom of the Netherlands

Pages from

100

Pages to

110

Pages count

11

URL

https://www.sciencedirect.com/science/article/pii/S0926224517300323

BibTex

@article{BUT140211,
  author="Miroslav {Doupovec} and Jan {Kurek} and Wlodzimierz {Mikulski}",
  title="Vertical functors on fibered manifolds",
  journal="DIFFERENTIAL GEOMETRY AND ITS APPLICATIONS",
  year="2017",
  volume="54",
  number="A",
  pages="100--110",
  doi="10.1016/j.difgeo.2017.03.005",
  issn="0926-2245",
  url="https://www.sciencedirect.com/science/article/pii/S0926224517300323"
}