\begin{definition}[Definition:Morphism]
Let $\mathbf C$ be a metacategory.
A '''morphism''' of $\mathbf C$ is an object $f$, together with:
* A domain $\operatorname{dom} f$, which is an object of $\mathbf C$
* A codomain $\operatorname{cod} f$, also an object of $\mathbf C$
The collection of all '''morphisms''' of $\mathbf C$ is denoted $\mathbf C_1$.
If $A$ is the domain of $f$ and $B$ is its codomain, this is mostly represented by writing:
:$f: A \to B$ or $A \stackrel{f}{\longrightarrow} B$
\end{definition}