nLab empty function

Contents

Definition

Given a set $X$ , the empty function to $X$ is a function

\varnothing \longrightarrow X

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.