On Tue, 02 Sep 2014 08:28:21 PM EDT, Timothy Revell <timothy.revell@strath.ac.uk> asked:
I'm wondering whether the category of ALL group actions is locally Cartesian closed. ...
Borrowing ideas from several earlier followups to this question, I might suggest the following as a quick and easy argument for a negative answer: 1) an initial object in that "category of ALL group actions" is given by the trivial group's action on the empty set, ({e}, 0); 2) the slice of that category over ({e}, 0) "is" just the category Grp of groups and group homomorphisms (well, really, it's the full subcategory of ALL group actions on the empty set :-) but that's essentially just Grp); 3) the category of group actions is no more a LCCC than Grp is a CCC. Or have I overlooked some obvious fly in my proposed ointment :-) ? Cheers, -- Fred Linton [For admin and other information see: http://www.mta.ca/~cat-dist/ ]