> I mean: without knowing something about the semantic of those methods, 
> how do we know that: 
>
>         sage: x.antipode() 
>
> will return an element of the algebra, and therefore the result shall 
> be retracted back, whereas: 
>
>         sage: x.counit() 
>
> will return an element of the ground field which needs no transformation? 
>
>
Ah, right, I agree (he says with a sheepish grin).
Andrew
 

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