Completing simple valuations in -categories

We prove that Keimel and Lawson's K-completion Kc of the simple valuation monad Vs defines a Kc∘Vs on each -category K. also characterise Eilenberg-Moore algebras as weakly locally convex K-cones, its algebra morphisms continuous linear maps. In addition, we explicitly describe distributive law over Kc, which allows us to show any (resp., convex, linear) topological cone is K-cone. give an example – Cantor tree with top shows dcpo-completion valuations not D-completion in general, where D category monotone convergence spaces