Equalizers and Coequalizers in the Category of Topological Molecular Lattices

A completely distributive complete lattice is called a molecular lattice. It is well known that the category TML of all topological molecular lattices with generalized order homomorphisms in the sense of Wang, is both complete and cocomplete. In this note, we give an example which shows that the structure of equalizers introduced by Zhao need not be true, in general. In particular, we present the structures of equalizers, coequalizers, monomorphisms and epimorphisms in this category.