%0 Journal Article
%T VB-algebroid morphisms and representations up to homotopy
%A Thiago Drummond
%A Madeleine Jotz
%A Cristian Ortiz
%J Mathematics
%D 2013
%I arXiv
%X We show in this paper that the correspondence between 2-term representations up to homotopy and $\mathcal{VB}$-algebroids, established by Gracia-Saz and Mehta, holds also at the level of morphisms, proving in particular that such correspondence is an equivalence of categories. As an application we study the relationship between IM-foliations on a Lie algebroid $A$ (the infinitesimal notion of ideal systems) and subrepresentations of the adjoint representation of $A$.
%U http://arxiv.org/abs/1302.3987v1