The monotone-light factorization for 2-categories via 2-preorders

João J. Xarez

It is shown that the reflection 2Cat --> 2PreOrd of the category of all 2-categories into the category of 2-preorders determines a monotone-light factorization system on 2Cat and that the light morphisms are precisely the 2-functors faithful on 2-cells with respect to the vertical structure. In order to achieve such result it was also proved that the reflection 2Cat --> 2Preord has stable units, a stronger condition than admissibility in categorical Galois theory, and that the 2-functors surjective both on horizontally and on vertically composable triples of 2-cells are the effective descent morphisms in 2Cat.

Keywords: Monotone-light factorization, 2-categories

2020 MSC: 18A32,18E50,18N10

Theory and Applications of Categories, Vol. 38, 2022, No. 31, pp 1209-1226.

Published 2022-10-25.

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