Exercise 2-61

Recall the symmetric monoidal preorder \(\mathbf{NMY} := (P,\leq, yes, min)\) from Exercise 2.34. Interpret what a NMY-category is.

Solution(1)

It is like a graph where some edges are ‘maybe’ edges. We can ask the question “Is there a path from a to b?" and if there is a true path we will get a ‘yes’. If the only paths are those which include maybe edges, then we get a ’maybe’. If there’s no path at all, we get a ‘no’.