Product preserving bundle functors on multifibered and multifoliate manifolds

TL;DR

This paper characterizes multifoliate structures via projective systems and fully describes all product preserving bundle functors on categories of multifibered and multifoliate manifolds.

Contribution

It establishes a correspondence between multifoliate structures and projective systems, and provides a complete classification of product preserving bundle functors.

Findings

Equivalence classes of multifoliate structures correspond to projective systems.

Complete description of all product preserving bundle functors.

Framework for analyzing multifibered and multifoliate manifolds.

Abstract

We show that the set of the equivalence classes of multifoliate structures is in one-to-one correspondence with the set of equivalence classes of finite complete projective systems of vector space epimorphisms. After that we give the complete description of all product preserving bundle functors on the categories of multifibered and multifoliate manifolds.