Convexities Generated by <Emphasis Type="Italic">L</Emphasis>-Monads

Let \mathbbF\mathbb{F} be a monad in the category Comp. We build for each \mathbbF\mathbb{F}-algebra a convexity in general sense (see van de Vel 1993). We investigate properties of such convexities and apply them to prove that the multiplication map of the order-preserving functional monad is soft.