nLab
strict initial object

Context

Category theory

Limits and colimits

Contents

Definition

An initial object \emptyset is called a strict initial object if any morphism xx\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)