Galois theory in variable categories
type: Item
instance of: scholarly article
title: Galois theory in variable categories
zbMATH Open document ID: 0801.18008
DOI: 10.1007/BF00872989
author: George Janelidze
author: Dietmar Schumacher
author: Ross H. Street
published in: Applied Categorical Structures
publication date: 1993-12-10T00:00:00Z
review text: The order reversing bijection between field extensions of \(K\) and subgroups of the Galois group \(G\) is a classical algebraic result. Grothendieck has shown that this bijection follows from the equivalence between the opposite of the category of étale algebras and the category of discrete \(G\)-spaces, throwing so a link between topos theory and classical Galois theory. This allowed extending Galois theory to more general rings and generalized spaces. In the present paper, the authors further generalize the Galois structures from ordinary categories to variable or indexed categories, so as to recapture in particular the well-known Joyal-Tierney theory, extending the Grothendieck Galois theory.
Mathematics Subject Classification ID: 18D30
Mathematics Subject Classification ID: 11R32
Mathematics Subject Classification ID: 18D35
Mathematics Subject Classification ID: 18D05
zbMATH DE Number: 458992
zbMATH Keywords: variable category
zbMATH Keywords: effective descent
zbMATH Keywords: Galois group
zbMATH Keywords: topos
zbMATH Keywords: indexed categories
Wikidata QID: Q55920391
reviewed by: F. Borceux
MaRDI profile type: Publication
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full work available at URL: https://doi.org/10.1007/bf00872989
OpenAlex ID: W2005125452
DBLP publication ID: journals/acs/JanelidzeSS93
description: scientific article; zbMATH DE number 458992