Original Articles

TRACES OF EPIMORPHISM CLASSES

Published in: Quaestiones Mathematicae
Volume 24 , issue 2 , 2001 , pages: 193–200

DOI: 10.1080/16073606.2001.9639207

Author(s): Lutz Schroder Department of Mathematics and Computer Science, University of Bremen, Bremen, Germany,

Keywords: Category , faithful functor , (extremal) epimorphism , retraction , semicategory

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.

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