Anindya - you gave a very nice answer to Puzzle 46 in #31 and #32. Congratulations!

There's another sort of answer where we look at a poset \$$A\$$ in which every \$$S\$$-tuple of elements has a join (for some fixed set \$$S\$$.) The join then defines a function

$$\bigvee: A^S \to A$$

This is a monotone function that's the left adjoint of the "generalized diagonal"

$$\Delta : A \to A^S$$