I will give a talk to undergraduate about the Tannakian formalism, and I'm looking for an nice example. More precisely I would like an example of a category $\mathcal C$ with a fiber functor $\omega$, giving an equivalence $\mathcal C \cong Rep(G)$ for a finite group $G$ (algebraic group is good too.)
Moreover, I would like that $\mathcal C$ is not too difficult to define.
For example, I know advanced examples (geometric Satake, or quantization of Lie bialgebras, or I think there is something in Tamas Szamuely's book) but they are definitely too advanced.
In addition of Joppy's comment, another nice example is given by the category of local systems on a connected manifold $X$, which is equivalent to $Rep(\pi_1(X,x_0))$. The fiber functor is given by $\omega(\mathcal L) = \mathcal L_{x_0}$ where $x_0 \in X$ is a given base point.