nLab
empty function

Contents

Contents

Definition

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.

Properties

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

Last revised on April 16, 2021 at 02:50:26. See the history of this page for a list of all contributions to it.