Well-behaved Epireflections for Kan Extensions

作者：Xarez Joao J^*

来源：Applied Categorical Structures, 2010, 18(2): 219-230.

DOI：10.1007/s10485-008-9148-1

• Kan extensions
• Cogenerating set
• Epireflection
• Stable units
• Prefactorization
• Monotone-light factorization
• Descent theory
• Galois theory
• Simplicial set
• Algebraic theory

Let K : B -> A be a functor such that the image of the objects in B is a cogenerating set of objects for A. Then, the right Kan extensions adjunction Set(K) (sic) Ran(K) induces necessarily an epireflection with stable units and a monotone-light factorization. This result follows from the one stating that an adjunction produces an epireflection in a canonical way, provided there exists a prefactorization system which factorizes all of its unit morphisms through epimorphisms. The stable units property, for the so obtained epireflections, is thereafter equivalently restated in such a manner it is easily recognizable in the examples. Furthermore, having stable units, there is a strong but quite simple sufficient condition for the existence of an associated monotone-light factorization, which has proved to be fruitful.

• 出版日期2010-4