A factorization of the Pumplün-Röhrl connection

Abstract The Galois connection given in 1985 by Pumplun and Rohrl between the classes of objects and the classes of morphisms in any category is shown (under ordinary circumstances) to have a “natural” factorization through the system of all idempotent closure operators over the category. Futhermore, each “component” of the factorization is a Galois connection in its own right. The first factor is obtained by using a generalization of the process, given by Salbany in 1975, that yields a closure operator for any class of topological spaces, while the second factor can be used to form the weakly hereditary core of an idempotent closure operator.