<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="7.x">Drupal-Biblio</source-app><ref-type>17</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Iakovos Androulidakis</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Crossed modules and the integrability of Lie brackets</style></title></titles><dates><year><style  face="normal" font="default" size="100%">2005</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">https://arxiv.org/abs/math/0501103</style></url></web-urls></urls><language><style face="normal" font="default" size="100%">eng</style></language><abstract><style face="normal" font="default" size="100%">&lt;span&gt;We show that the integrability obstruction of a transitive Lie algebroid coincides with the lifting obstruction of a crossed module of groupoids associated naturally with the given algebroid. Then we extend this result to general extensions of integrable transitive Lie algebroids by Lie algebra bundles. Such a lifting obstruction is directly related with the classification of extensions of transitive Lie groupoids. We also give a classification of such extensions which differentiates to the classification of transitive Lie algebroids discussed in \cite{KCHM:new}.&lt;/span&gt;</style></abstract></record></records></xml>