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    TOWARDS A 2-DIMENSIONAL NOTION OF HOLONOMY
    (Amer Inst Mathematical Sciences-Aims, 2022) BROWN, R. O. N. A. L. D.; ICEN, I. L. H. A. N.
    Previous 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.