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 known as
An initial object is also known as a coterminal object.