Movability and co-movability of shape morphisms

TL;DR

This paper introduces new notions of movability for morphisms in inverse systems, extending existing properties and ensuring compatibility with pro-morphisms and shape morphisms, supported by examples and applications.

Contribution

It defines and explores movability concepts for morphisms of inverse systems, enhancing the theoretical framework of shape theory.

Findings

New movability notions for morphisms are proposed.

Properties and examples illustrate the concepts.

Applications demonstrate practical relevance.

Abstract

The purpose of this paper is to define some notions of movability for morphisms of inverse systems which extend the movability properties of inverse systems and which are compatible with the equivalence relations which define pro-morphisms and shape morphisms. Some properties, examples and applications are given.