It is an initial object in the category of all categories.

Creating the initial "objects" is difficult, especially for programmers who are used to designing the old-fashioned way.

It should not be confused with the zero or bottom type, which allows no values and is the initial object in this category.

They can be characterized as initial objects in the category of co-cones from F.

Dually, the coproduct of an empty family is an initial object.

In the category of non-empty sets, there are no initial objects.

Note that even though some of the hom-sets are empty, the category Ring is still connected since it has an initial object.

As a result, the empty set is the unique initial object of the category of sets and functions.

This works in the dual case, with a category of cocones having an initial object.

In category theory, 0 is sometimes used to denote an initial object of a category.