group algebra

There is likewise a natural categorification of the group algebra \(\mathbb{C}[\Gamma]\), namely the monoidal category \(\mathcal{D}(G)\) of \(\mathcal{D}\) -modules on the group \(G\) under convolution.

• Categorified: monoidal categories of sheaves on G with convolution

For a finite group, carries the structure of a symmetric Frobenius algebra