\begin{definition}[Definition:Initial Object]
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 $0 \to C$.
\end{definition}