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 also formulate the notion of a differential tensor category, and a version of the Tannakian formalism for differential linear groups, and show how the same techniques can be used to deduce the analogous results in that context.
- Pub Date:
- August 2009
- Mathematics - Logic;
- Mathematics - Category Theory;
- Mathematics - Representation Theory;
- 25 pages. Paper reorganised, some of the main results are stated more clearly. The part going in the other direction (deducing the model theoretic statement using category theory) moved to arxiv:1012.3185