Pointfree funcoids between join-semilattices conjecture

Today I’ve come up with the following easy to prove theorem (exercise!) for readers of my book: Theorem If there exists at least one pointfree funcoid from a poset $latex \mathfrak{A}$ to a poset $latex \mathfrak{B}$ then either both posets have least element or none of them. This provokes me to the following conjecture also: […]