# nLab strict initial object

category theory

## Applications

#### Limits and colimits

limits and colimits

# Contents

## Definition

An initial object $\emptyset$ is called a strict initial object if any morphism $x\to \emptyset$ must be an isomorphism.

## Examples

The initial objects of a poset, of Set, Cat, Top, and of any topos (more generally of any extensive category) are strict.

At the other extreme, a zero object is only a strict initial object if the category is trivial (equivalent to the terminal category).

Revised on August 30, 2013 10:39:13 by Ingo Blechschmidt (137.250.162.16)