Terminal Object

In Category Theory, an object \(i\) in a category \(C\) is said to be terminal if for every \(c \in C\), there exists a unique morphism \(c \to i\). The converse notion is an initial object.

Examples of Terminal Objects

1. In the category of sets, every singleton set is terminal.
2. Likewise in \(\text{Top}\).
3. In a preorder, a terminal object is a global maximum.