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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
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.

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Additional Information

Christopher F. Townsend
Affiliation: 8 Aylesbury Road, Tring, Hertfordshire, HP23 4DJ, United Kingdom

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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