Initial object

In category theory, an initial object is one for which there exists precisely one arrow from it to every other object in the category. The dual concept is the terminal object.

Definition

An initial object in a category $𝐂$ is an object $0$ such that there exists a unique morphism $0\to x$ for every $𝐂$-object $x$.[cite:@maclane2000categories]

Examples

• In $𝐒𝐞𝐭$, the initial object is the empty set.