Applied Categorical Structures

, Volume 1, Issue 1, pp 103–110 | Cite as

Galois theory in variable categories

  • George Janelidze
  • Dietmar Schumacher
  • Ross Street
Article

Abstract

The order-reversing bijection between field extensions and subgroups of the Galois group G follows from the equivalence between the opposite of the category of étale algebras and the category of discrete G-spaces [2]. We show that the basic ingredient for this equivalence of categories, and for various known generalizations, is a factorization system for variable categories.

Mathematics Subject Classifications (1991)

18D30 11R32 18D35 18D05 

Key words

Variable category Galois group topos indexed category parametrized category homomorphism of bicategories effective descent internal category 

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Copyright information

© Kluwer Academic Publishers 1993

Authors and Affiliations

  • George Janelidze
    • 1
  • Dietmar Schumacher
    • 2
  • Ross Street
    • 3
  1. 1.Mathematics InstituteAcademy of ScienceTbilisi
  2. 2.Mathematics DepartmentAcadia UniversityWolfvilleCanada
  3. 3.Mathematics DepartmentMacquarie UniversityAustralia

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