Solution(1)
Take the two monoidal monotone maps from Exercise 2.44
f yields a discrete preorder whereas g does not.
Find a different monoidal monotone map \(\mathbf{Cost}\xrightarrow{g}\mathbf{Bool}\) from the one in Example 2.65. Using the construction from Proposition 2.64, convert a Lawvere metric space into two different preorders. Find a metric space for which this happens.NOCARD
Take the two monoidal monotone maps from Exercise 2.44
f yields a discrete preorder whereas g does not.