Model theory and the tannakian formalism

We draw the connection between the model theoretic notions of internality and the binding group on one hand, and the Tannakian formalism on the other. More precisely, we deduce the fundamental results of the Tannakian formalism by associating to a Tannakian category a first order theory, and applying the results on internality there. We then formulate the notion of a differential tensor category, which axiomatises the category of differential representations of differential linear groups, and show how the model theoretic techniques can be used to deduce the analogous results in that context.