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

• Autor(a) principal: Xarez, João J.
• Data de Publicação: 2022
• Tipo de documento: Artigo
• Idioma: eng
• Título da fonte: Repositório Científico de Acesso Aberto de Portugal (Repositórios Cientìficos)
• Texto Completo: http://hdl.handle.net/10773/35180
• topic: Monotone-light factorization; 2-categories

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.