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A short proof of the localic groupoid representation of Grothendieck toposes


Author: Christopher F. Townsend
Journal: Proc. Amer. Math. Soc. 142 (2014), 859-866
MSC (2010): Primary 06D22
DOI: https://doi.org/10.1090/S0002-9939-2013-11829-0
Published electronically: December 20, 2013
MathSciNet review: 3148520
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Abstract: It is known that each Grothendieck topos is the category of $ \mathbb{G}$-equivariant sheaves for some localic groupoid $ \mathbb{G}$. A simple proof of this is given which relies on the recently observed fact that the pullback adjunction between locales induced by any geometric morphism satisfies Frobenius reciprocity.


References [Enhancements On Off] (What's this?)

  • [J02] Peter T. Johnstone, Sketches of an elephant: a topos theory compendium. Vol. 1, Oxford Logic Guides, vol. 43, The Clarendon Press, Oxford University Press, New York, 2002. MR 1953060 (2003k:18005)
  • [JT84] André Joyal and Myles Tierney, An extension of the Galois theory of Grothendieck, Mem. Amer. Math. Soc. 51 (1984), no. 309, vii+71. MR 756176 (86d:18002)
  • [T10] Christopher F. Townsend, A representation theorem for geometric morphisms, Appl. Categ. Structures 18 (2010), no. 6, 573-583. MR 2738511 (2012h:06024), https://doi.org/10.1007/s10485-009-9187-2

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Additional Information

Christopher F. Townsend
Affiliation: 8 Aylesbury Road, Tring, Hertfordshire, HP23 4DJ, United Kingdom
Email: info@christophertownsend.org

DOI: https://doi.org/10.1090/S0002-9939-2013-11829-0
Received by editor(s): November 4, 2011
Received by editor(s) in revised form: April 24, 2012
Published electronically: December 20, 2013
Communicated by: Lev Borisov
Article copyright: © Copyright 2013 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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