By the way: Proposition 2.20 in the book says that any symmetric monoidal preorder \$$\mathcal{V}\$$ has an opposite \$$\mathcal{V}^{\text{op}}\$$; completing the proof of this result is [Exercise 2.21](https://forum.azimuthproject.org/discussion/1983/exercise-21-chapter-2/p1), and then in [Exercise 2.22](https://forum.azimuthproject.org/discussion/1984/exercise-22-chapter-2/p1) you're invited to study \$$\mathbf{Cost}^{\text{op}}\$$. Everyone should give them a try!