Principal bundles as Frobenius adjunctions with application to geometric morphisms
2015 ◽
Vol 159
(3)
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pp. 433-444
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AbstractUsing a suitable notion of principalG-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.
1985 ◽
Vol 37
(3)
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pp. 442-451
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2008 ◽
Vol 212
(1)
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pp. 175-192
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Keyword(s):
2012 ◽
Vol 10
(2)
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pp. 299-369
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Keyword(s):
Keyword(s):
1997 ◽
Vol 30
(6)
◽
pp. 2027-2054
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1997 ◽
pp. 165-184
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