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.
Keywords: Cat-groups, factorization systems in a 2-category.
2000 MSC: 18A32, 18D05, 18D10, 18G99, 20L05.
Theory and Applications of Categories, Vol. 7, 2000, No. 5, pp 47-70.