This entry is about the article
Catégories Tannakiennes,
Grothendieck Festschrift, vol. II,
Birkhäuser Progress in Math. 87 (1990) pp.111-195.
(pdf)
The main theorem is a Tannakian reconstruction theorem, which repairs a problem in the book
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
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