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Principal bundles as Frobenius adjunctions with application to geometric morphisms

Published online by Cambridge University Press:  12 August 2015

CHRISTOPHER TOWNSEND
CHRISTOPHER TOWNSEND*
Affiliation:
8 Gordon Villas, Aylesbury Road, Tring, Hertfordshire, HP23 4DJ. e-mail: info@christophertownsend.org
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Abstract

Using a suitable notion of principal G-bundle, defined relative to an arbitrary cartesian category, it is shown that principal bundles can be characterised as adjunctions that stably satisfy Frobenius reciprocity. The result extends from internal groups to internal groupoids. Since geometric morphisms can be described as certain adjunctions that are stably Frobenius, as an application it is proved that all geometric morphisms, from a localic topos to a bounded topos, can be characterised as principal bundles.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 3 , November 2015 , pp. 433 - 444
Copyright
Copyright © Cambridge Philosophical Society 2015 

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