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Factorization systems for symmetric cat-groups

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S. Kasangian and E.M. Vitale

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.

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