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It is shown that the reflection 2Cat --> 2Preord of the category of all2-categories into the category of 2-preorders determines a monotone-lightfactorization system on 2Cat and that the light morphisms are precisely the2-functors faithful on 2-cells with respect to the vertical structure. In orderto achieve such result it was also proved that the reflection 2Cat --> 2Preordhas stable units, a stronger condition than admissibility in categorical Galoistheory, and that 2-functors surjective both on horizontally composable triplesof vertically composable pairs and on vertically composable triples ofhorizontally composable pairs of 2-cells are effective descent morphisms in2Cat.

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