Definition. Preorder [math-O6C8]

We usual define a preorder is a set $X$ with a binary relation $\le$, where the relation is reflexive and transitive.

Every preorder can also be viewed as a small category, where all composition morphism of $A \to B$ and $B \to C$ is the unique morphism $A \to C$. Or we say there is at most one morphism from one object to another.