Dear Tim, Write Act for the category you mention. Then Act/(G,0) is clearly equivalent to Grp/G. Since Grp/G is not cartesian closed, neither is Act/(G,0). Regards, Steve Lack. On 1 Sep 2014, at 7:12 pm, Timothy Revell <timothy.revell@strath.ac.uk> wrote:
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.
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