Topological representation of lattice homomorphisms (Q897422)

The authors state that if \(\mathbf{NLat}\) denotes the category of normal and distributive lattices with \(\mathbf{0}\) and \(\mathbf{1}\) and homomorphisms, and \(\mathbf{Comp}\) denotes the category of compact Hausdorff spaces and continuous mappings, then there exists a contravariant functor \(Ult:\mathbf{NLat} \rightarrow \mathbf{Comp}\), which when restricted to the subcategory of Boolean lattices coincides with the functor known from the theory of Stone Duality. Furthermore it carries monomorphisms into surjections, but need not carry epimorphisms into injections. They then illustrate how the result can be used to obtain several classical topological theorems.