Dear All, I'm wondering whether the category of ALL group actions is locally Cartesian closed. This is NOT the functor category [G,Set] for some category G with one object, since we allow G to vary. To be more specific the category is as follows. - The objects are pairs (G,X), where G is a group and X is a G-Set. - A morphism (G,X) -> (G', X') is given by a pair (h,f), where h:G->G' is a group homomorphism and f: X -> X' is a function (a morphism in Set) such that for all g in G, x in X h(g) * f(x) = f(g * x) where * on the left denotes the group action of G' on X' and * on the right denotes the group action of G on X. All the best, Tim -- Timothy Revell, Department of Computer and Information Sciences, University of Strathclyde. The University of Strathclyde is a charitable body, registered in Scotland, with registration number SC015263. [For admin and other information see: http://www.mta.ca/~cat-dist/ ]