Is the category of group actions LCCC?

[Timothy Revell <timothy.revell@strath.ac.uk>]

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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