Transitive quasi-uniform structures depending on a parameter.

In a category C with an (E , M )-factorization structure for morphisms, we prove that any subclass N of M which is closed under pullbacks determines a transitive quasi-uniform structure on C . In addition to providing a categorical characterization of all transitive quasi-uniform structures compatible with a topology, this result also permits us to establish a number of Galois connections related to quasi-uniform structures on C . These Galois connections lead to the description of subcategories of C determined by quasi-uniform structures. Several examples considered at the end of the paper illustrate our results. [ABSTRACT FROM AUTHOR]