Functorial prolongations of Lie groupoids

Volume 76 / 2007

Ivan Kolář Banach Center Publications 76 (2007), 177-184 MSC: 58A20, 58A32. DOI: 10.4064/bc76-0-7

Abstract

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 ${\cal F} \Phi$ over $M$. Every action of $\Phi$ on a fibered manifold $Y\to M$ is extended to an action of ${\cal F} \Phi$ on $FY\to M$.

Authors

  • Ivan KolářFaculty of Science
    Masaryk University
    Janáčkovo nám. 2a
    602 00 Brno, Czech Republic
    e-mail

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