2-范畴通过2-预序的单调-光分解
The monotone-light factorization for 2-categories via 2-prorders
AI总结：
本文通过2-预序反射在2-范畴上建立单调-光分解系统，证明光态射为垂直结构上2-胞腔忠实的2-函子，并验证稳定单位及有效下降态射条件。
摘要：
本文证明了所有2-范畴的范畴到2-预序范畴的反射 2Cat --> 2Preord 在2Cat上确定了一个单调-光分解系统，并且光态射恰好是那些在垂直结构上对2-胞腔忠实的2-函子。为了获得这一结果，还证明了反射 2Cat --> 2Preord 具有稳定单位，这是比范畴伽罗瓦理论中的可容许性更强的条件，并且对水平可复合的三元组（由垂直可复合的二元组构成）以及对垂直可复合的三元组（由水平可复合的二元组构成）均满射的2-函子是2Cat中的有效下降态射。
英文摘要：
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.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
