Brown, RIçen, I2024-08-042024-08-0420030001-8708https://doi.org/10.1016/S0001-8708(02)00074-9https://hdl.handle.net/11616/93594Previous work (Pradines, C. R. Acad. Sci. Paris 263 (1966) 907; Aof and Brown, Topology Appl. 47 (1992) 97) has given a setting for a holonomy Lie groupoid of a locally Lie groupoid. Here we develop analogous 2-dimensional notions starting from a locally Lie crossed module of groupoids. This involves replacing the Ehresmann notion of a local smooth coadmissible section of a groupoid by a local smooth coadmissible homotopy (or free derivation) for the crossed module case. The development also has to use corresponding notions for certain types of double groupoids. This leads to a holonomy Lie groupoid rather than double groupoid, but one which involves the 2-dimensional information. (C) 2003 Elsevier Inc. All rights reserved.eninfo:eu-repo/semantics/openAccesscrossed modulehomotopydouble groupoidlinear sectionLie groupoidsholonomyArticle178114117510.1016/S0001-8708(02)00074-92-s2.0-0042428783N/AWOS:000184648800004Q1