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Precategories and Galois theory

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Category Theory

Part of the book series: Lecture Notes in Mathematics ((LNM,volume 1488))

Abstract

We give a new version of Galois theory in categories in which normal extensions are replaced by arbitrary extensions for which the “pullback functor” is monadic, and their Galois groupoids are replaced by internal pregroupoids; we obtain the “fundamental theorem of Galois theory” using just simple remarks on internal precategories and change of universe for internal functors.

I would like to thank Aurelio Carboni at Milan University for inviting me for extended visit in Summer 1990 during which the work on this paper was completed.

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References

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Author information

Authors and Affiliations

  1. Mathematical Institute of the Georgian, Academy of Sciences, Z. Rukhadze str. 1, 380093, Tbilisi, Georgia

    George Janelidze

Authors
  1. George Janelidze
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Editor information

Aurelio Carboni Maria Cristina Pedicchio Guiseppe Rosolini

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© 1991 Springer-Verlag

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Janelidze, G. (1991). Precategories and Galois theory. In: Carboni, A., Pedicchio, M.C., Rosolini, G. (eds) Category Theory. Lecture Notes in Mathematics, vol 1488. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0084218

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  • DOI: https://doi.org/10.1007/BFb0084218

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-54706-8

  • Online ISBN: 978-3-540-46435-8

  • eBook Packages: Springer Book Archive

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