Affine mobi spaces

TL;DR

This paper explores affine mobi spaces, establishing an isomorphism between R-modules and pointed affine mobi spaces over a mobi algebra R when R is a unital ring with 2 invertible, linking algebraic and geometric models.

Contribution

It demonstrates a categorical isomorphism between R-modules and affine mobi spaces under specific algebraic conditions, advancing the understanding of mobi space structures.

Findings

Isomorphism between R-modules and affine mobi spaces

Conditions for the isomorphism when R is a unital ring with 2 invertible

Analysis of affine mobi spaces as models for geodesic spaces

Abstract

The category of mobi algebras has been introduced as a model to the unit interval of real numbers. The notion of mobi space over a mobi algebra has been proposed as a model for spaces with geodesic paths. In this paper we analyse the particular case of affine mobi spaces and show that there is an isomorphism of categories between R-modules and pointed affine mobi spaces over a mobi algebra R as soon as R is a unitary ring in which 2 is an invertible element.