Definition:Initial Object

Definition
Let $\mathbf C$ be a metacategory.

An initial object of $\mathbf C$ is an object $0 \in \mathbf C_0$ of $\mathbf C$ such that:


 * For all $C \in \mathbf C_0$, there is a unique morphism $0 \to C$.

Also see

 * Initial Object is Unique
 * Terminal Object