Geodesic
The monotone-light factorization for 2-categories via 2-preorders
Theory and applications of categories, Tome 38 (2022), pp. 1209-1226

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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.

Publié le :
Classification : 18A32, 18E50, 18N10
Keywords: Monotone-light factorization, 2-categories 
@article{TAC_2022_38_a30,
     author = {Jo\~ao J. Xarez},
     title = {The monotone-light factorization  for 2-categories via 2-preorders},
     journal = {Theory and applications of categories},
     pages = {1209--1226},
     publisher = {mathdoc},
     volume = {38},
     year = {2022},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2022_38_a30/}
}
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João J. Xarez. The monotone-light factorization  for 2-categories via 2-preorders. Theory and applications of categories, Tome 38 (2022), pp. 1209-1226. http://geodesic.mathdoc.fr/item/TAC_2022_38_a30/