Sophie wrote:

> I'm also wondering about Marius's suggestion that \\( f\\) should satisfy

> \\(1_Y\leq_Y f(1_X)\\)

I don't think this condition plays any role in Puzzle 77. There's an interesting asymmetry in the definition of "monoidal preorder": the operation \\(\otimes\\) needs to get along with relation \\(\le\\), but the unit \\(1\\) does not.

Later we will meet various kinds of _maps_ between monoidal preorders: see Section 2.2.5. These should remind you of Puzzle 77, and they involve conditions on the unit. They are definitely relevant to your "pricing of groceries" examples... but nonetheless, I don't think any conditions on the unit are relevant to Puzzle 77.

I could be wrong.

> I'm also wondering about Marius's suggestion that \\( f\\) should satisfy

> \\(1_Y\leq_Y f(1_X)\\)

I don't think this condition plays any role in Puzzle 77. There's an interesting asymmetry in the definition of "monoidal preorder": the operation \\(\otimes\\) needs to get along with relation \\(\le\\), but the unit \\(1\\) does not.

Later we will meet various kinds of _maps_ between monoidal preorders: see Section 2.2.5. These should remind you of Puzzle 77, and they involve conditions on the unit. They are definitely relevant to your "pricing of groceries" examples... but nonetheless, I don't think any conditions on the unit are relevant to Puzzle 77.

I could be wrong.