Definition:Order Category/Definition 2

Definition

Let $\mathbf C$ be a metacategory.

Then $\mathbf C$ is an order category if and only if:

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.

Also see

• Equivalence of Definitions of Order Category

• Results about order categories can be found here.