Dan wrote:

> [John](https://forum.azimuthproject.org/profile/17/John%20Baez)
I was having a hard time proving [puzzle 83](https://forum.azimuthproject.org/discussion/2098/lecture-27-chapter-2-adjoints-of-monoidal-monotones#latest)
and I think it's because the unit conditions are the other way around for the lax and oplax monotones, respectively:

> - For the lax monotone we should require:
\\( I_Y \le f(I_X) . \\)

> - For the oplax monotone we should require:
\\( f(I_X) \le_Y I_Y . \\)

> And a nitpick: one of these equations was using \\(1\\) rather than \\(I\\) to denote the unit; I've noticed this notation is also mixed at the end of the [next lecture](https://forum.azimuthproject.org/discussion/2098/lecture-27-chapter-2-adjoints-of-monoidal-monotones#latest).

You're right on all of these! I'm fixing these mistakes now. It's important to get those inequalities pointing the right way. Thanks!