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Functorial prolongations of Lie groupoids. (English) Zbl 1115.58003

Kubarski, Jan (ed.) et al., Geometry and topology of manifolds. The mathematical legacy of Charles Ehresmann. On the occasion of the hundredth anniversary of his birthday. Proceedings of the conference, Bȩdlewo, Poland, May 8–15, 2005. Warsaw: Polish Academy of Sciences, Institute of Mathematics. Banach Center Publications 76, 177-184 (2007).
Summary: For every Lie groupoid \(\Phi\) with \(m\)-dimensional base \(M\) and every fiber product preserving bundle functor \(F\) on the category of fibered manifolds with \(m\)-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps, we construct a Lie groupoid \(\mathcal F \Phi\) over \(M\). Every action of \(\Phi\) on a fibered manifold \(Y\to M\) is extended to an action of \(\mathcal F \Phi\) on \(FY\to M\).
For the entire collection see [Zbl 1112.57300].

MSC:

58A20 Jets in global analysis
58A32 Natural bundles
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