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• CommentRowNumber1.
• CommentAuthorUrs
• CommentTimeApr 16th 2021

added mentioning of the generalization of “empty function” to “empty morphism” as any morphism out of a strict initial object

• CommentRowNumber2.
• CommentAuthorDmitri Pavlov
• CommentTimeApr 16th 2021
• (edited Apr 16th 2021)

There is a contradiction between what this entry says:

The empty function to the empty set is not a constant function.

and what the entry constant function says:

More generally, any function f:S→T is a constant function if f(a)=f(b) for every element a and element b of S.

In fact, constant function contradicts empty function even more directly:

If S and T are both empty, then the unique function from S to T is constant, but not constant at any particular value.

• CommentRowNumber3.
• CommentAuthorMike Shulman
• CommentTimeApr 16th 2021

I guess constant function should be generalized to mention the two different notions of constant morphism, and this page should say that the empty function is constant in one sense but not the other.