# Generalized congruences -- Epimorphisms in Cat

## Marek A. Bednarczyk, Andrzej M. Borzyszkowski, Wieslaw Pawlowski

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 ${\cal C}at$. Extremal, regular and various other classes of epimorphic functors are characterized and inter-related.

Keywords: congruence, epimorphic functor, coequalizer, category of small categories.

1991 MSC: 18A05, 18A20, 18A30, 18A32, 18B99.

Theory and Applications of Categories, Vol. 5, 1999, No. 11, pp 266-280.

http://www.tac.mta.ca/tac/volumes/1999/n11/n11.dvi
http://www.tac.mta.ca/tac/volumes/1999/n11/n11.ps
http://www.tac.mta.ca/tac/volumes/1999/n11/n11.pdf
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1999/n11/n11.dvi
ftp://ftp.tac.mta.ca/pub/tac/html/volumes/1999/n11/n11.ps

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