Vector bundles over Lie groupoids and algebroids
  We study VB-groupoids and VB-algebroids, which are vector bundles in the realm of Lie groupoids and Lie algebroids. Through a suitable reformulation of their definitions, we elucidate the Lie theory relating these objects, i.e., their relation via differentiation and integration. We also show how to extend our techniques to describe the more general Lie theory underlying double Lie algebroids and LA-groupoids. 
Henrique Bursztyn, Alejandro Cabrera, Matias del Hoyo
math.DG math.SG