An alibi (for map object)

Let’s say I have a set called domain D and a set called codomain C

D = {d}, C = {c}

I can now think of functions from the domain D to the codomain C.  There is one.

d |– f –> c

Let’s see how much trouble we can get this one into.

This one must have something to do with one element in both domain and codomain

1 ^ 1 = 1

expressed in terms of properties of the structures involved: domain set, codomain set, and the set of functions.  How, then, are the structures-themselves (domain D, codomain C, functions f: D -> C) related?

Welcome to map object!  (OK, this is how close we can let object get to map.)