Great, so this rather complicated condition is exactly the necessary and sufficient one!

By the way, there's more about grocery store prices in [Lecture 27](https://forum.azimuthproject.org/discussion/2098/lecture-27-chapter-2-adjoints-of-monoidal-monotones/p1). I hadn't realized until teaching this course how much category theory, or at least poset theory, is lurking in the humble corner grocery store.