A note on the algebraic representation of coframes via the Scott closed set monad over the category of S0-convex spaces

Abstract

In this note, we shall give a complete answer to the question that what kind of lattice structures corresponds to the T-algebras with respect to the Scott closed set monad over the category of S0-convex spaces and show that the Eilenberg-Moore algebras with respect to the Scott closed set monad are precisely coframes endowed with the Scott convex structure. Meanwhile, we shall also prove that the category of coframes is strictly monadic over the category of S0-convex spaces.