Galois theory in symmetric monoidal categories
type: Item
instance of: scholarly article
title: Galois theory in symmetric monoidal categories
zbMATH Open document ID: 0936.18009
author: George Janelidze
author: Ross H. Street
published in: Journal of Algebra
publication date: 2000-05-14T00:00:00Z
review text: 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''.
Mathematics Subject Classification ID: 18D10
zbMATH DE Number: 1356296
zbMATH Keywords: Tannaka duality
zbMATH Keywords: Galois theory
zbMATH Keywords: symmetric monoidal category
reviewed by: Lindsay N. Childs
MaRDI profile type: Publication
full work available at URL: jabr.1999.7905
OpenAlex ID: W2076406344
Wikidata QID: Q56687274
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DOI: 10.1006/JABR.1999.7905
description: scientific article; zbMATH DE number 1356296