A Tannakian context for Galois theory

Strong similarities have been long observed between the Galois and Tannaka theories of the representation of groups. In this paper we construct an explicit (neutral) Tannakian context for the Galois theory of atomic topoi and prove equivalence for the fundamental theorem. Since the theorem is known...

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Autores principales: Dubuc, E.J., Szyld, M.
Formato: JOUR
Materias:
Atomic topos
Grothendieck-Galois
Locale-valued bijections
Tannaka
Acceso en línea:http://hdl.handle.net/20.500.12110/paper_00018708_v234_n_p528_Dubuc
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
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spelling todo:paper_00018708_v234_n_p528_Dubuc2023-10-03T13:52:19Z A Tannakian context for Galois theory Dubuc, E.J. Szyld, M. Atomic topos Grothendieck-Galois Locale-valued bijections Tannaka Strong similarities have been long observed between the Galois and Tannaka theories of the representation of groups. In this paper we construct an explicit (neutral) Tannakian context for the Galois theory of atomic topoi and prove equivalence for the fundamental theorem. Since the theorem is known for the Galois context, this yields a proof of the fundamental (recognition) theorem for a new Tannakian context. This example is different from the additive cases or their generalization for which the theorem is known to hold and for which the unit of the tensor product is always an object of finite presentation, which is not the case in our context. © 2012 Elsevier Ltd. JOUR info:eu-repo/semantics/openAccess http://creativecommons.org/licenses/by/2.5/ar http://hdl.handle.net/20.500.12110/paper_00018708_v234_n_p528_Dubuc
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Atomic topos
Grothendieck-Galois
Locale-valued bijections
Tannaka
spellingShingle Atomic topos
Grothendieck-Galois
Locale-valued bijections
Tannaka
Dubuc, E.J.
Szyld, M.
A Tannakian context for Galois theory
topic_facet Atomic topos
Grothendieck-Galois
Locale-valued bijections
Tannaka
description Strong similarities have been long observed between the Galois and Tannaka theories of the representation of groups. In this paper we construct an explicit (neutral) Tannakian context for the Galois theory of atomic topoi and prove equivalence for the fundamental theorem. Since the theorem is known for the Galois context, this yields a proof of the fundamental (recognition) theorem for a new Tannakian context. This example is different from the additive cases or their generalization for which the theorem is known to hold and for which the unit of the tensor product is always an object of finite presentation, which is not the case in our context. © 2012 Elsevier Ltd.
format JOUR
author Dubuc, E.J.
Szyld, M.
author_facet Dubuc, E.J.
Szyld, M.
author_sort Dubuc, E.J.
title A Tannakian context for Galois theory
title_short A Tannakian context for Galois theory
title_full A Tannakian context for Galois theory
title_fullStr A Tannakian context for Galois theory
title_full_unstemmed A Tannakian context for Galois theory
title_sort tannakian context for galois theory
url http://hdl.handle.net/20.500.12110/paper_00018708_v234_n_p528_Dubuc
work_keys_str_mv AT dubucej atannakiancontextforgaloistheory
AT szyldm atannakiancontextforgaloistheory
AT dubucej tannakiancontextforgaloistheory
AT szyldm tannakiancontextforgaloistheory
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