The Category of Topological De Morgan Molecular Lattices

Abstract

The concept of topological molecular lattices was introduced by Wang
as a generalization of ordinary topological spaces, fuzzy topological spaces and L-fuzzy
topological spaces in terms of closed elements, molecules, remote neighbourhoods and
generalized order homomorphisms. In our previous work, we introduced the concept of
generalized topological molecular lattices in terms of open elements and investigated
some properties of them. In this paper, we dene and consider the category TDML
whose objects are topological De Morgan molecular lattices and whose morphisms are
continuous generalized order homomorphisms such that its right adjoins preserve the
pseudocomplement operation. We show that this category is complete and cocomplete.
In particular, we characterize products, coproducts, equalizers and coequalizers. Also,
we show that the category TOP of all topological spaces is a re
ective and core
ective
subcategory of TDML.