Extended Galois theory and dissonant morphisms
type: Item
instance of: scholarly article
title: Extended Galois theory and dissonant morphisms
zbMATH Open document ID: 0936.18006
DOI: 10.1016/S0022-4049(98)00113-3
author: George Janelidze
author: Walter Tholen
published in: Journal of Pure and Applied Algebra
publication date: 2000-05-14T00:00:00Z
review text: Let \(\mathcal C\) be a category (for which a Galois structure is given) and \(p:E\to B\) an effective descent morphism in \(\mathcal C\). In this paper the notion of weakly split object over \((E,p)\) is introduced and the category of such objects is described in terms of internal actions of the Galois (pregroupoid) \((E,p)\) with an additional structure. Various known results in categorical Galois theory are obtained as special cases. Finally an elaborate list of examples and applications is given.
Mathematics Subject Classification ID: 18B99
Mathematics Subject Classification ID: 18A99
Mathematics Subject Classification ID: 18A20
Mathematics Subject Classification ID: 13B05
Mathematics Subject Classification ID: 57M10
Mathematics Subject Classification ID: 18A32
Mathematics Subject Classification ID: 18A40
Mathematics Subject Classification ID: 18B40
zbMATH DE Number: 1384150
zbMATH Keywords: descent morphism
zbMATH Keywords: split object
zbMATH Keywords: categorical Galois theory
reviewed by: I. Tofan
MaRDI profile type: Publication
full work available at URL: s0022-4049(98)00113-3
OpenAlex ID: W2056269838
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description: scientific article; zbMATH DE number 1384150