@John

From Lecture 17:
>A similar argument shows that joins are really right adjoints! If \$$A \$$ is a poset with all binary meets, we get a monotone function

>$\vee : A \to A \times A$

>that's the _right_ adjoint of \$$\Delta \$$. This is just a clever way of saying

>$a \le b \textrm{ and } a \le b' \textrm{ if and only if } a \le b \wedge b'$

>which is also easy to check.

Is there something mixed up here? From the flow of everything it seems like joins should be meet? And also if \$$\wedge \$$ is going to be right adjoint of \$$\Delta\$$ shouldn't it go in the opposite direction of \$$\Delta \$$ ie. \$$\wedge : A \times A \to A \$$? or am I missing something here?