@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?

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?