category has enough injectives.

Sometimes we deal with the categories of $(R,G)$–modules –denoted as ${{}_{(R,G)}\,\mathcal M}$, where $R$ is a rational commutative $G$–module algebra. We say that $M$ is an $(R,G)$–module, provided that it is a rational $G$–module, a module over the ring $R$ and that the actions are related in the following manner if $x \in G\,,\, r \in R\,,\,m\in M$, $x\cdot (rm)=(x\cdot r)(x \cdot m)$. The morphisms are defined in the obvious way.

Antecedents, faithfull representations of Lie groups
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The concerns that led to the discovery of the concept of observability, seem to derive from the persuit of the understanding and simplification of a series of results on the existence of faithful finite dimensional representations of Lie groups (due to E. Cartan, M. Goto, D. Ado, A. Malcev, K. Iwasawa, G. Hochschild and others).

Below we trace backwards the main steps of this process.

Previously to the results appearing in ERA, Hochschild and Mostow published in 1957/58 two important papers ([@kn:homolie; @kn:mostow]) on the extension of representations of Lie groups that are cited explicitly in the aforementioned introduction of ERA:

The differences between the algebraic case and the Lie group situation are remarkable and it is patent 