Galois theory in symmetric monoidal categories (Q1806098)

The Galois theory for symmetric monoidal categories presented here is a special case of the categorical Galois theory developed by the authors and \textit{D. Schumacher} [Appl. Categ. Struct. 1, 103-110 (1993; Zbl 0801.18008)] but more general than that of \textit{G. Janelidze} [Lect. Notes Math. 1488, 157-173 (1991; Zbl 0754.18002)]. The Galois theory here, plus Deligne's splitting theorem, yields Tannaka duality. In the author's words, ``we show how to replace all the other elaborate machinery of \textit{P. Deligne} [``Catégories tannakiennes'', in: Grothendieck Festschrift, Vol. II, Prog. Math. 87, 111-195 (1990; Zbl 0727.14010)] by categorical Galois theory''.