nLab weakly initial object

Definition

An object in a category is weakly initial if there exists a morphism from it to every other object in the category.

(So a weakly initial object is an actual initial object if this morphism is unique.)

Weak initiality is an instance of a weak colimit. It is also an instance of a weakly initial set that happens to be a singleton set.

Related concepts

• strict initial object

References

Weak adjoint functors along with weak colimits, with weakly initial objects as a special case, were defined in:

• Paul Kainen, Weak adjoint functors, Mathematische Zeitschrift 122 1 (1971) 1-9 [dml:171575]

See also:

• Philip Wadler, Recursive types for free!