Traces of Epimorphism Classes

Abstract

Classes of morphisms that occur as preimages of the class
of all epimorphisms, 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.
Mathematics Subject Classification (1991): 18A10, 18A20, 18A22, 18A32
Keywords: category, faithful functor, (extremal) epimorphism, retraction,
semicategory, graphs, diagram schemes, precategories, neocategories, epimorphisms,
monomorphisms, special classes of morphisms, null morphisms, factorization,
categories, special properties of functors, factorization of morphisms, substructures,
quotient structures, congruences, amalgams, open

Quaestiones Mathematicae
24(2) 2001, 193-200