Adjoints between posets are (monotone or antitone) Galois connections; monads correspond to closure operators; what is a [two-variable adjunction](https://ncatlab.org/nlab/show/two-variable+adjunction) in this low-categorical setting?


I'm able to write the bare definition, of course. What I seek is intuition, and possibly an instance of this structure, on a triple of poset $P,Q,R$, possibly under a different name.



Two variable adjunctions in poset-categories
One important special case of a 2-variable adjunction is a biclosed monoidal structure on a category, such as a cartesian closed category. A cartesian closed poset (with finite joins as well) is called a [Heyting algebra](https://ncatlab.org/nlab/show/Heyting%20algebra), and corresponds to intuitionistic logic in the same way that Boolean algebras correspond to classical logic. In particular, every Boolean algebra is a Heyting algebra and hence is equipped with a biclosed monoidal structure.


