Closure Operator Constructions Depending On One Parameter

Abstract

Let X be an (E , M)-category for sinks. For each subclass N of M, two new Galois connections that generalize the Clementino-Tholen connectedness and separation Galois connections are introduced. In particular, closure operator constructions that generalize the regular and coregular closure operators are given. A big diagram of several different types of Galois connections is built. The usefulness of the dependence on the parameter N is shown in that many previously obtained closure constructions can be deduced from the diagram by choosing N in different ways.