  We give an account of lax orthogonal factorisation systems on order-enriched
categories. Among them, we define and characterise the KZ-reflective ones, in a
way that mirrors the characterisation of reflective orthogonal factorisation
systems. We use simple monads to construct lax orthogonal factorisation
systems, such as one on the category of T_0 topological spaces closely related
to continuous lattices.
