well, it is a function in the ordinary sense. The domain is the set of 0tuples of which there is exactly one denoted (), or since we're only thinking about sets, we may as well denote it @, or anything else we may care to use. Thus we're looking at the space of all functions in the proper sense from the set {@} to the set Y. Any function from a set with one element to any set S takes a unique value,so we can identify the set of all functions with Y. Just as we can always identify maps(X,Y) with Y^X.
The more general concept of maps are called morphisms, btu now i come to look at the question more closely I realize it was completely unnecessary to even allude to them.
