Definition:Category of Ordered Sets

Definition
The category of posets, denoted $\mathbf{Pos}$, is the metacategory with:


 * objects: All posets;
 * morphisms: All monotone mappings.

This forms a metacategory, as shown on Category of Posets is Category.

Note
The reason to call $\mathbf{Set}$ a metacategory is foundational; allowing it to be a category would bring us to axiomatic troubles.