20 Apr
2012
20 Apr
'12
5:02 a.m.
Wren,
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?
Good question. I'd suppose that they should be parametrized by any (Abelian?) group on the weights/multiplicities, where (+) is the canonical one since we're talking about "negative" membership.
Any groupoid on the multiplicities would do, I guess. As I wrote in my answer to Richard, max seems a better choise, as it nicely generalises mapping on sets. Cheers, Stefan