|Closure operation. I am not sure how much this has in common with its namesake in "computere science".
Remember that we can treat partially-ordered sets and their order-preserving functions as categories and functors?
A monotonous (order-preserving) function C: X → X is called closure if
∀x∊X x <= C(x) and C(C(x)) = C(x).
These two conditions are exactly what monad axioms turn into when applied to a partially ordered set - meaning that monads in partially ordered sets are just closures. We can also try to apply this to the partially ordered set of paths in a graph.
(skip difficult part)