arXiv subjects
Publications and source records attributed to I. Icen.
We give a detailed description of the structure of the actor 2-crossed module related to the automorphisms of a crossed module of groupoids. This generalises work of Brown and Gilbert for the case of crossed modules of groups, and part of this is needed for work on 2-dimensional holonomy to be developed elsewhere (see math.DG/0009082).
The notion of local subgroupoid as a generalisation of a local equivalence relation was defined in a previous paper by the first two authors. Here we use the notion of star path connectivity for a Lie groupoid to give an important new class of examples, generalising the local equivalence relation of a foliation, and develop in this new context basic properties of coherence, due earlier to Rosenthal in the special case. These results are required for further applications to holonomy and monodromy.