nLab
strict initial object

Contents

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 and even any distributive 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).

Last revised on May 3, 2018 at 18:44:50. See the history of this page for a list of all contributions to it.