Factorization systems for symmetric cat-groups

Kasangian, Stefano;Vitale, Enrico
(2000) Theory and Applications of Categories — Vol. 7, p. 47-70 (2000)

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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 catgroups 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.
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Kasangian, S., & Vitale, E. (2000). Factorization systems for symmetric cat-groups. Theory and Applications of Categories, 7, 47-70. https://hdl.handle.net/2078.5/152051 (Original work published 2000)