\begin{definition}[Definition:Order Category/Definition 2]
Let $\mathbf C$ be a metacategory.
Then $\mathbf C$ is an '''order category''' {{iff}}:
:For all objects $C, C'$ of $\mathbf C$, there is at most one morphism $f: C \to C'$
:Whenever $f: C \to C'$ is an isomorphism, $C = C'$
Thus, an '''order category''' is a skeletal preorder category.
\end{definition}