nLab empty function





The basis of it all

 Set theory

set theory

Foundational axioms

foundational axioms

Removing axioms



Given a set XX, the empty function to XX is a function

X \varnothing \longrightarrow X

toXX from the empty set.

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 that 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.

Last revised on February 27, 2024 at 05:44:52. See the history of this page for a list of all contributions to it.