Functorial prolongations of Lie groupoids
Volume 76 / 2007
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 $FY\to M$.
