This question was prompted since I read that category theory can be seen as a generalization of representation theory.
Tanaka duality basically states that from the category of representations of a group, we can recover the original group.
The Yoneda's Lemma states that the functor $$ \mathcal{C} \to \mathbf{Fun}(\mathcal{C}^{opp},\mathbf{Set}) : X \mapsto h_X $$ is fully faithful.
I have heard that functors to $\mathbf{Set}$ can be interpreted as representations of an arbitrary category $\mathcal{C}$ into the category $\mathbf{Set}$. Thus, it seems to me that the Yoneda Lemma states something roughly similar to Tanaka duality, namely that the category $\mathcal{C}$ can be reconstructed from the category of its representations.
Is this correct? Can Yoneda be seen as a more abstract version of Tanaka duality? I am trying to understand better the precise relation between these two important theorems, and in more general between category theory and representation theory. Any input or enlightenment is welcome on this topic.