[math] \newcommand{\mathds}{\mathbb}[/math]

Look up the Doplicher-Roberts and Deligne theorems, stating that the compact group [math]G[/math] can be in fact recovered from the sole knowledge of the category [math]\mathcal R_G[/math], with no need for the embedding into [math]\mathcal H[/math], and write down a brief account of this.