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 Well-behaved Epireflections for Kan Extensions
Please use this identifier to cite or link to this item http://hdl.handle.net/10773/7081

title: Well-behaved Epireflections for Kan Extensions
authors: Xarez, JJ
keywords: Kan extensions
Cogenerating set
Epireflection
Stable units
Prefactorization
Monotone-light factorization
Descent theory
Galois theory
Simplicial set
Algebraic theory
issue date: 2010
publisher: Springer Verlag
abstract: 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.
URI: http://hdl.handle.net/10773/7081
ISSN: 0927-2852
publisher version/DOI: http://dx.doi.org/10.1007/s10485-008-9148-1
source: Applied Categorical Structures
appears in collectionsCIDMA - Artigos

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