Geodesic
Factorization systems for symmetric cat-groups
Theory and applications of categories, Tome 7 (2000), pp. 47-70

Voir la notice de l'article provenant de la source Theory and Applications of Categories website

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.

Classification : 18A32, 18D05, 18D10, 18G99, 20L05.
Keywords: Cat-groups, factorization systems in a 2-category. 
@article{TAC_2000_7_a4,
     author = {S. Kasangian and E.M. Vitale},
     title = {Factorization systems for symmetric cat-groups},
     journal = {Theory and applications of categories},
     pages = {47--70},
     publisher = {mathdoc},
     volume = {7},
     year = {2000},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2000_7_a4/}
}
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S. Kasangian; E.M. Vitale. Factorization systems for symmetric cat-groups. Theory and applications of categories, Tome 7 (2000), pp. 47-70. http://geodesic.mathdoc.fr/item/TAC_2000_7_a4/