Relations among the category of topological molecular lattices and certain related categories (Q1368196)

Let \({\mathbf {TOP}}\) be the category of topological spaces with continuous mappings as morphisms, \({\mathbf {TML}}\) the category of topological molecular lattices with continuous order homomorphisms as morphisms [\textit{G. Wang}, Sci. Sin., Ser. A 27, 785-798 (1984; Zbl 0599.54005)] and \({\mathbf {PBT}}\) the category of bitopological spaces which are locally ultracompact and sober in one of the two topologies with bicontinuous mappings quasi-open in that topology as morphisms. The authors show that \({\mathbf {TOP}}\) is a both monomorphic coreflexive and epimorphic reflexive subcategory of \({\mathbf {TML}}\) and that \({\mathbf {TML}}\) is equivalent to \({\mathbf {PBT}}\).