Model theory and the Tannakian formalism
Abstract
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.
 Publication:

arXiv eprints
 Pub Date:
 August 2009
 DOI:
 10.48550/arXiv.0908.0604
 arXiv:
 arXiv:0908.0604
 Bibcode:
 2009arXiv0908.0604K
 Keywords:

 Mathematics  Logic;
 Mathematics  Category Theory;
 Mathematics  Representation Theory;
 03C65;
 20G05
 EPrint:
 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