Dear Bill and Ronnie, In the context of topos theory it is very natural to consider groupoids both for Galois toposes as for the van Kampen theorems. See Marta Bunge, "Galois groupoids and Covering Morphisms in Topos Theory", Fields Institute Communications, volume 4 (2004) 131-161. I will be happy to send anyone interested a pdf file of this paper. I quote from the Introduction: "Also in section 4 we introduce and study the notion of a Galois topos over an arbitrary base topos S. Although these relative Galois toposes are not assumed to be either connected or pointed, they come naturally equipped with a bag of points indexed by the connected components of a (non-connected) universal cover; this is in line with the view advocated by Grothendieck and Brown that, rather than a single base point, one ought to work with a suitable "paquet des points", for instance, one that is invariant under the symmetries in the given situation. This idea was naturally and independently incorporated into topos theory both by Kennison and myself, by discussing the fundamental groupoid of an unpointed (and possibly pointless) locally connected topos." The justification for these statements are given in detail in the paper. Here is the outline: 1. Introduction. 2. Locally constant objects in toposes. 3. Stack completions and the fundamental groupoid of a topos. 4. Galois groupoids and Galois toposes. 5. Locally paths simply connected toposes over an arbitrary base. 6. Generalized covering morphisms and a van Kampen theorem. References. With best regards, Marta ************************************************ Marta Bunge Professor Emerita Dept of Mathematics and Statistics McGill University 805 Sherbrooke St. West Montreal, QC, Canada H3A 2K6 Office: (514) 398-3810/3800 Home: (514) 935-3618 marta.bunge@mcgill.ca http://www.math.mcgill.ca/~bunge/ ************************************************ [For admin and other information see: http://www.mta.ca/~cat-dist/ ]