Cabras, Antonella, Kolář, Ivan, Modugno, Marco
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Summary: [For the entire collection see Zbl 0742.00067.]A general theory of fibre bundles structured by an arbitrary differential-geometric category is presented. It is proved that the structured bundles of finite type coincide with the classical associated bundles.
Peter Michor (1984)
Cahiers de Topologie et Géométrie Différentielle Catégoriques
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Daniel Canarutto (2000)
Archivum Mathematicum
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Smooth bundles, whose fibres are distribution spaces, are introduced according to the notion of smoothness due to Frölicher. Some fundamental notions of differential geometry, such as tangent and jet spaces, Frölicher-Nijenhuis bracket, connections and curvature, are suitably generalized. It is also shown that a classical connection on a finite-dimensional bundle naturally determines a connection on an associated distributional bundle.