Transitive quasi-uniform structures depending on a parameter

In a category C with an (epsilon,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.