Towards a 2-dimensional notion of holonomy

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Previous work (Pradines, 1966, Aof and Brown, 1992) has given a setting for a holonomy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for the crossed module case. The development also has to use corresponding notions for certain types of double groupoids. This leads to a holonomy Lie groupoid rather than double groupoid, but one which involves the 2-dimensional information.
30 pages, A4, xypic, epic, eepic

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Differential Geometry, Category Theory, 18D05, 58H05, 22A22, 22E99

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http://salesiana.dossiersoluciones.com/handle/123456789/59894

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/math/0009082
 http://arxiv.org/abs/math/0009082

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arXiv