Galois theory in variable categories

George Janelidze; Dietmar Schumacher; Ross Street

doi:10.1007/BF00872989

Galois theory in variable categories

George Janelidze^*, Dietmar Schumacher, Ross Street

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

4 Citations (Scopus)

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.

Original language	English
Pages (from-to)	103-110
Number of pages	8
Journal	Applied Categorical Structures
Volume	1
Issue number	1
DOIs	https://doi.org/10.1007/BF00872989
Publication status	Published - Mar 1993

Keywords

effective descent
Galois group
homomorphism of bicategories
indexed category
internal category
Mathematics Subject Classifications (1991): 18D30, 11R32, 18D35, 18D05
parametrized category
topos
Variable category

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10.1007/BF00872989

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title = "Galois theory in variable categories",

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 {\'e}tale 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.",

keywords = "effective descent, Galois group, homomorphism of bicategories, indexed category, internal category, Mathematics Subject Classifications (1991): 18D30, 11R32, 18D35, 18D05, parametrized category, topos, Variable category",

author = "George Janelidze and Dietmar Schumacher and Ross Street",

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doi = "10.1007/BF00872989",

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T1 - Galois theory in variable categories

AU - Janelidze, George

AU - Schumacher, Dietmar

AU - Street, Ross

PY - 1993/3

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N2 - 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.

AB - 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.

KW - effective descent

KW - Galois group

KW - homomorphism of bicategories

KW - indexed category

KW - internal category

KW - Mathematics Subject Classifications (1991): 18D30, 11R32, 18D35, 18D05

KW - parametrized category

KW - topos

KW - Variable category

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U2 - 10.1007/BF00872989

DO - 10.1007/BF00872989

M3 - Article

AN - SCOPUS:0009280194

SN - 0927-2852

VL - 1

SP - 103

EP - 110

JO - Applied Categorical Structures

JF - Applied Categorical Structures

IS - 1

ER -

Galois theory in variable categories

Abstract

Keywords

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