Initial Object

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

Examples of Initial Objects

1. In the category of sets, the empty set is initial.
2. Likewise in \(\text{Top}\).
3. In a preorder, an initial object is a global minimum.