> > The very purpose of the category framework it to declare in a  
> > mathematical
> > way, this that have a matematical meaning. In the case of a right  
> > action of A
> > on B, on declare that B is a A-RightModule. It is much more  
> > informative by all
> > respect than testing if a random element of A accept to be  
> > multiplied by a
> > random element of B.
> 
> _rmul_ and _lmul_ are only tried if B is an A-module. (We don't (yet)  
> have the distinction between right and left modules, this is part of  
> where the "try it out" comes into play).

Thanks for this explanation... Should I understand that once we had the
correct framework, these are supposed to disappear ?  

> However, not all actions are module actions, e.g. a permutation  
> acting on an ordered list, or a matrix acting on a quadratic form (to  
> take two examples that I've been thinking about lately).

Permutations acting on lists is not a module structure but this may fits in a
category of sets with a group acting on (G-set) no-linearity here. For acting
on plain list, (i.e. data structure I would rather not use "*" do denote the
operation).

For matrix on quadratic form I don't see the problem. But maybe I'm not
thinking about the same operation as you.

Cheers,

Florent

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