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\begin{document}$K:\mathbb{B}\rightarrow \mathbb{A}$\end{document} be a functor such that the image of the objects in \documentclass[12pt]{minimal}
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\begin{document}$\mathbb{B}$\end{document} is a cogenerating set of objects for \documentclass[12pt]{minimal}
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\begin{document}$\mathbb{A}$\end{document}. Then, the right Kan extensions adjunction \documentclass[12pt]{minimal}
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\begin{document}$\mathbf{Set}^K\dashv Ran_K$\end{document} 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.
