TRACES OF EPIMORPHISM CLASSES

Abstract

Classes of morphisms that occur as preimages of the class of all epi-morphisms, of all extremal epimorphisms, respectively of all retractions under some faithful functor are characterized by suitable closure properties. The corresponding question for regular or strict epimorphisms is presented as an open problem. A further application of the methods developed in this context yields a similar characterization of classes of morphisms that are final with respect to some faithful functor.