A posetal prop is a prop that is also a poset.
In other words, a symmetric monoidal preorder \((\mathbb{N}, \leq)\) for some posetal relation \(\leq\), where the monoidal product is addition.
Give three examples of a posetal prop.
The normal meaning of \(\leq\) as less than or equal to
The divisibility relation
The opposite of the first example (greater than or equal to).