Sjoerd,
>>>> For a specific example, I haven't the faintest intuition about
>>>> what 'map' should do. Suppose we have
>>>> {(k1)x1, (k2)x2}
>>>> and f x1 == f x2 = y. Should the value of map f {...} be
>>>> {(k1+k2)y} or {(k1`max`k2)y} or what?
> I don't think max would be a good choice, as that would mean that the default
> multiplicity would have to be negative infinity (the identity element of max)
> instead of 0, and then using Int as the type for multiplicity would not cut
> it.
Why would one need such an identity element for map?
Note that the monoidal structure isn't defined over the "maximum of
multiplicites" but over the "maximum of *nonzero* multiplicites". (For ordinary
sets and ordinary multisets these operations happen to coincide.)
Cheers,
Stefan
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