nLab Catégories Tannakiennes

This entry is about the article

on Tannakian categories.

The main theorem is a Tannakian reconstruction theorem, which repairs a problem in the book

  • N. Saavedra Rivano, Catégories Tannakiennes, Springer LNM 265, 1972

which had a substantial gap in the proof of the main theorem.

At the end of the article there is an application to the differential Galois theory (which has been earlier much studied by A. R. Magid) which is the Galois theory for differential rather than algebraic equations.

The article had a huge influence not only in Tannakian theory but also in creating more technical exchange between the modern algebraic geometry with category theory and bi(al)gebras.

In the followup

  • Pierre Deligne, Catégorie Tensorielle, Moscow Math. Journal 2 (2002) no. 2, 227-248. (pdf)

the conditions for Tannakian reconstruction are relaxed further, see at Deligne's theorem on tensor categories.

Generalization to “non-neutral” Tannakian categories, and representations of gerbes is in

See also

category: reference

Last revised on November 25, 2016 at 18:06:33. See the history of this page for a list of all contributions to it.