Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
   
Mobile Device Pairing
Green Open Access
Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

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
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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?)


Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC (2010): 06D22

Retrieve articles in all journals with MSC (2010): 06D22


Additional Information

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

DOI: http://dx.doi.org/10.1090/S0002-9939-2013-11829-0
PII: S 0002-9939(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.