How do I define a function between finite sets within the category
framework? Should the following work?
sage: S = Set([1,2,3])
sage: T = Set([4,5,6,7])
sage: f = S.hom(lambda x: 3+x, T)
sage: f
Generic morphism:
From: {1, 2, 3}
To: {4, 5, 6, 7}
sage: f(2)
---------------------------------------------------------------------------
TypeError Traceback (most recent call
last)
....
TypeError: 2 fails to convert into the map's domain {1, 2, 3}, but a
`pushforward` method is not properly implemented
I see that it works if I define S and T using FiniteEnumeratedSet instead.
Is that the best solution?
Or suppose I want to define a map sending 1 to 5, 2 to 7, 3 to 5. I can't
see how to use the dictionary {1:5, 2:7, 3:5} (for example) to define a
function.
In general, I would like fully functional, callable, composable morphisms
of sets, and finite sets are good enough for now. Any advice? Also of other
categories, in particular finite abelian groups, but maybe those work
better already?
--
John
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