Fibered Correspondence

TL;DR

This paper explores fibered correspondences, focusing on reduced fibered correspondences and their properties, including fibered equivalence and isomorphism theorems, within the context of bundles and their relationships.

Contribution

It introduces the concept of reduced fibered correspondence and establishes fibered equivalence and isomorphism theorems for fibered morphisms.

Findings

Reduced fibered correspondence is only between fibers over the same base point.

Fibered equivalence and isomorphism theorems are established for fibered morphisms.

Composition of fibered correspondences may not always be defined.

Abstract

Base of fibered correspondence is arbitrary correspondence. Fibered correspondence is interesting when we consider relationship between different bundles. However composition of fibered correspondences may not always be defined. Reduced fibered correspondence is defined only between fibers over the same point of base. Reduced fibered correspondence in bundle is called 2-ary fibered relation. We considered fibered equivalence and isomorphism theorem in case of fibered morphisms.