Abstract
Mobi algebras and mobi spaces were introduced as algebraic structures capturing interpolation phenomena. Affine mobi spaces are known to be equivalent to modules over rings with one half, suggesting that mobi spaces may be viewed as an extension of module theory beyond linear geometry.
In this paper we revisit both notions. We show that the axioms of a mobi space can be simplified and we provide a geometric interpretation of the fundamental composition axiom. We further prove that, whenever the underlying mobi algebra admits an inverse of one half, every pointed mobi space induces a commutative loop together with a family of scalar operators satisfying natural analogues of the basic module identities. The affine condition is precisely what recovers the classical module structure.
These results support the view that mobi spaces provide an algebraic framework for interpolation beyond the linear setting.