Definition:Order Category/Definition 2

Definition
Let $\mathbf C$ be a metacategory.

Then $\mathbf C$ is a poset 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, a poset category is a skeletal preorder category.

Also see

 * Preorder Category