论文标题
通过2-核的2类别的单调轻度分解
The monotone-light factorization for 2-categories via 2-prorders
论文作者
论文摘要
结果表明，所有两类类别的反射2CAT-> 2个preord to of 2 peorters的类别确定了2CAT上的单调轻度分解系统，并且光形态恰好是对垂直结构的2个型号的2个功能。为了实现这一结果，还证明了反射2CAT - > 2个preord具有稳定的单元，比分类Galois理论中的可接受性更强，并且在水平垂直组合的同进的三倍上，在垂直综合的成对和垂直综合的三倍上均具有2 cepsot的摩尔斯克式2杯摩尔斯式，这两个功能均具有垂直合成的三元组合的三倍。
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 2-functors surjective both on horizontally composable triples of vertically composable pairs and on vertically composable triples of horizontally composable pairs of 2-cells are effective descent morphisms in 2Cat.
