A short proof of the localic groupoid representation of Grothendieck toposes
HTML articles powered by AMS MathViewer
- by Christopher F. Townsend PDF
- Proc. Amer. Math. Soc. 142 (2014), 859-866 Request permission
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
- 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
- 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, DOI 10.1090/memo/0309
- Christopher F. Townsend, A representation theorem for geometric morphisms, Appl. Categ. Structures 18 (2010), no. 6, 573–583. MR 2738511, DOI 10.1007/s10485-009-9187-2
Additional Information
- Christopher F. Townsend
- Affiliation: 8 Aylesbury Road, Tring, Hertfordshire, HP23 4DJ, United Kingdom
- Email: info@christophertownsend.org
- 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
- © Copyright 2013
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - Journal: Proc. Amer. Math. Soc. 142 (2014), 859-866
- MSC (2010): Primary 06D22
- DOI: https://doi.org/10.1090/S0002-9939-2013-11829-0
- MathSciNet review: 3148520