Simple reflections, revisited.

We present a notion of simple monad that generalises the notion of simple reflection of Cassidy-Hebert-Kelly to order-enriched categories, and study the factorisations they induce. These factorisations are lax orthogonal and can be characterised by a cancellation property. We will show that filter monads on topological T0-spaces are simple, and show that the factorisations they induced, are lax orthogonal.