Smooth Manifolds vs Differential triads

Abstract

We consider differentiable maps in the setting of Abstract Differential Geometry and we study the conditions that ensure the uniqueness of differentials in this setting. In particular, we prove that smooth maps between smooth manifolds admit a unique differential, coinciding with the usual one. Thus smooth manifolds form a full subcategory of the category of differential triads, a result with physical implications.

14 pages, to be published in "Revue Roumaine de Mathématique Pures et Appliquées"