We clarify how the natural transformations of fiber product preserving bundle functors on can be constructed by using reductions of the rth order frame bundle of the base, being the category of fibered manifolds with m-dimensional bases and fiber preserving maps with local diffeomorphisms as base maps. The iteration of two general r-jet functors is discussed in detail.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-8, author = {Ivan Kol\'a\v r}, title = {Natural maps depending on reductions of frame bundles}, journal = {Annales Polonici Mathematici}, volume = {101}, year = {2011}, pages = {83-90}, zbl = {1229.58004}, language = {en}, url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-8} }
Ivan Kolář. Natural maps depending on reductions of frame bundles. Annales Polonici Mathematici, Tome 101 (2011) pp. 83-90. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ap102-1-8/