BROWN, R. O. N. A. L. D.ICEN, I. L. H. A. N.2024-08-042024-08-0420221941-48891941-4897https://doi.org/10.3934/jgm.2022011https://hdl.handle.net/11616/100768Previous 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.eninfo:eu-repo/semantics/openAccessCrossed modulehomotopydouble groupoidlinear sectionLie groupoidsholonomyArticle14233135710.3934/jgm.20220112-s2.0-85133442053Q3WOS:000809583000001Q4