The group action category stuff would be nice, but you would run into 
exactly the same question that Dima asked: What are you going to do if 
there is more than one possible action. You'll have to either use some 
heuristics (take the simpler / less nested action) or raise some exception 
telling the user to explicitly disambiguate between them. 



On Monday, March 25, 2013 8:33:57 AM UTC+1, tom d wrote:
>
> Hm, wouldn't this just be a direct product of the individual group 
> actions?  It seems to me that we're expecting the permutations to act 
> according to an 'obvious' group action.  Should we also expect 'obvious' 
> actions of things like a dihedral group when given a 2-dimensional vector?  
> Probably the answer is to generalize and build up a proper group actions 
> category (with obvious methods passing to representations!).

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