Generalized congruences — Epimorphisms in Cat
Marek A. Bednarczyk, Andrzej M. Borzyszkowski, Wiesław Pawłowski · Theory and applications of categories · 1999
ABSTRACT. The paper generalizes the notion of a congruence on a category and pursues some of its applications. In particular, generalized congruences are used to provide a concrete construction of coequalizers in Cat. Extremal, regular and various other classes of epimorphic functors are characterized and inter-related. 1.