For every Lie groupoid Φ 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 ℱ Φ over M. Every action of Φ on a fibered manifold Y → M is extended to an action of ℱ Φ on FY → M.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-7,
author = {Ivan Kol\'a\v r},
title = {Functorial prolongations of Lie groupoids},
journal = {Banach Center Publications},
volume = {75},
year = {2007},
pages = {177-184},
zbl = {1115.58003},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-7}
}
Ivan Kolář. Functorial prolongations of Lie groupoids. Banach Center Publications, Tome 75 (2007) pp. 177-184. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc76-0-7/