In category theory, an object "1" is a terminal (or final) object if for every object A, there is exactly one morphism from A to 1.

In the category of sets and functions, every singleton set {*a*} is a terminal object. The morphism in this case is the constant function mapping everything to *a*, that is, *f*(*x*)=*a*.

In a partially ordered set, considered as a category, the maximum (if it exists) is a terminal object.

Terminal objects are dual to initial objects.