Bill, I'm sorry that I give a bad example.
About the axioms that "map" has to fullfill:
map(id, x) === x for all x
map(f, map(g,x)) === map(compose(f,g), x) for all x, f, g
Of course it's possible to have a Functor(E)
for AbelianMonoidRing(R,E), it may not "make sense",
but it is doable, so it is important to have a documentation
for map in each domain that implements it.
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