  In this paper we question the status of TEGR, the Teleparallel Equivalent of
General Relativity,as a gauge theory of translations. We observe that TEGR (in
its usual translation-gauge view) does not seem to realize the generally
admitted requirements for a gauge theory for some symmetry group $G$: namely it
does not present a mathematical structure underlying the theory which relates
to a principal $G$-bundle and the choice of a connection on it (the gauge
field). We point out that, while it is usually presented as absent, the gauging
of the Lorentz symmetry is actually present in the theory, and that the choice
of an Erhesmann connection to describe the gauge field makes the translations
difficult to implement (mainly because there is in general no principal
translation-bundle). We finally propose to use the Cartan Geometry and the
Cartan connection as an alternative approach, naturally arising from the
solution of the issues just mentioned, to obtain a more mathematically sound
framework for TEGR.
