Contents

foundations

# Contents

## Definition

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

$\varnothing \longrightarrow X$

to$X$ 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 06:50:26. See the history of this page for a list of all contributions to it.