  In this paper we address the general problem of including inflationary models
exhibiting Starobinsky-like potentials into (symmetric) $\mathcal{N}=2$
supergravities. This is done by gauging suitable abelian isometries of the
hypermultiplet sector and then truncating the resulting theory to a single
scalar field. By using the characteristic properties of the global symmetry
groups of the $\mathcal{N}=2$ supergravities we are able to make a general
statement on the possible $\alpha$-attractor models which can obtained upon
truncation. We find that in symmetric $\mathcal{N}=2$ models group theoretical
constraints restrict the allowed values of the parameter $\alpha$ to be
$\alpha=1,\,\frac{2}{3},\, \frac{1}{3}$. This confirms and generalizes results
recently obtained in the literature. Our analysis heavily relies on the
mathematical structure of symmetric $\mathcal{N}=2$ supergravities, in
particular on the so called $c$-map connection between Quaternionic K\"ahler
manifolds starting from Special K\"ahler ones. A general statement on the
possible consistent truncations of the gauged models, leading to
Starobinsky-like potentials, requires the essential help of Tits Satake
universality classes. The paper is mathematically self-contained and aims at
presenting the involved mathematical structures to a public not only of
physicists but also of mathematicians. To this end the main mathematical
structures and the general gauging procedure of $\mathcal{N}=2$ supergravities
is reviewed in some detail.
