International Journal of Mathematics and Mathematical Sciences
Volume 2003 (2003), Issue 23, Pages 1465-1480
doi:10.1155/S0161171203111064
Abstract
Given a Lie groupoid Ω, we construct a groupoid J1Ω equipped with a universal connection from which all the
connections of Ω are obtained by certain pullbacks. We show
that this general construction leads to universal connections on
principal bundles (considered by García (1972)) and
universal linear connections on vector bundles (ultimately
related with those of Cordero et al. (1989)).