[Sophie](https://forum.azimuthproject.org/profile/2225/Sophie%20Libkind), you gave the following example in favor of the definition from Lecture 26:

> Define \$$f: \mathbb Z \to \mathbb R\$$ by \$$f(x) = x+ 1\$$. It has a right adjoint \$$g: \mathbb R \to \mathbb Z\$$ defined by \$$g(y) = \lfloor y-1 \rfloor\$$.

But it seems to me that for this particular example both definitions are consistent with the super-theorem:

- According to the definitions from lecture 26, \$$f\$$ is oplax and \$$g\$$ is lax (as you have just showed).
- According to the definitions from lecture 27, \$$f\$$ is not oplax, \$$f(0) = 1 \nleq 0\$$, and \$$g\$$ is not lax, \$$0 \nleq -1 = g(0)\$$.