basic constructions:
strong axioms
further
Given a set , the empty function to is a function
This always exists and is unique; in other words, the empty set is an initial object in the category of sets.
If regarded as a bundle, the empty function is the empty bundle over its codomain.
In generalization to ambient categories other than Sets, an empty morphism would be any morphism out of a strict initial object.
The empty function to the empty set is not a constant function, though it is a weakly constant function.