Abstract
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.
Publisher
Cambridge University Press (CUP)
Reference12 articles.
1. T. Plewe Localic triquotient maps are effective descent maps. Math. Proc. Camb. Phil. Soc. 122, No. 01 (Cambridge University Press, 1997), 17–43.
2. I. Moerdijk Classifying toposes and foliations. Ann. Inst. fourier (Grenoble). 41, no. 1 (1991), p. 189–209.
3. A. Kock Fibre bundles in general categories. J. Pure Appl. Algebra. 56, 3 (1989), 233–245.
4. P. T. Johnstone Sketches of an elephant: a topos theory compendium. Vols 1, 2, Oxford Logic Guides 43, 44 (Oxford Science Publications, 2002).
5. M. Bunge An application of descent to a classification theorem for toposes. Math. Proc. Camb. Phil. Soc. 107 (1990), pp 59–79.
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