This question of mine arises from my reading of the quite-helpful-for-me, posted answers to the question:
In the Set category, why is every singleton a terminal object? Especially helpful for me was the answer posted by @Lærne : https://math.stackexchange.com/a/2820583
But I have a gap in my understanding. I know that the 𝚂𝚎𝚝 category is the category whose objects are sets, and whose morphisms from some set A to some set B are the functions from A to B. I know that in general, in a category, there is no requirement for there to be a morphism from an object to another distinct object. I understand why, if there does indeed exist a function from an object (set) A to a singleton set, then that function is unique. But I don't understand why, in the first place, a function needs to exist from an object (set) A to a singleton set.