Re: local homeomorphisms, and etendues Comment on Feldman's description of binary products in the category of spaces and local homeomorphisms. The product of an object X with itself is always the (object of arrows of) a groupoid, usually a rather uninteresting one. But in the category of spaces and local homeomorphisms, it is a very interesting groupoid, usually denoted \Gamma X (the pseudogroup of (germs of) local automorphisms of X, considered by Haefliger (and others?) back in the 1950's. It is also a groupoid in the category of spaces and all continuous maps, since pull-backs are preserved by the forgetful functor. For similar reasons, X times Y is a principal bundle over the groupoid \Gamma X (acting from the left), and \Gamma Y (acting from the right). Similar considerations apply in the category of locales. The corresponding localic groupoids were in essence considered by Ehresmann in "Gattungen von lokalen Strukturen", under the name of _local_ groupoids. I presented an expose about this, and its relatinship to etendue theory at the PSSL in Sussex in March, and the manuscript I circulated, may be picked up by ftp from theory.doc.ic.ac.uk, directory papers/Kock. It is called sussex.dvi. Anders Kock