This paper is a first step in the study of symmetric cat-groups as the 2-dimensional analogue of abelian groups. We show that a morphism of symmetric cat-groups can be factorized as an essentially surjective functor followed by a full and faithful one, as well as a full and essentially surjective functor followed by a faithful one. Both these factorizations give rise to a factorization system, in a suitable 2-categorical sense, in the 2-category of symmetric cat-groups. An application to exact sequences is given.
Theory and Applications of Categories, Vol. 7, 2000, No. 5, pp 47-70 http://www.tac.mta.ca/tac/volumes/7/n5/n5.dvi http://www.tac.mta.ca/tac/volumes/7/n5/n5.ps ftp://ftp.tac.mta.ca/pub/tac/html/volumes/7/n5/n5.dvi ftp://ftp.tac.mta.ca/pub/tac/html/volumes/7/n5/n5.psTAC Home