Weak reflections and weak factorization systems
Mathematics & Actuarial Science Department
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Applied Categorical Structures
We describe a one-to-one correspondence between saturated weak factorization systems and weak reflections in categories C with finite products. This actually extends to an adjunction between the category of natural weak factorization systems on C (in the sense of Grandis and Tholen, Arch Math 42:397-408, 2006, and Garner, arXiv preprint, 2007) and the category of monads on C . Explicit comparisons are made with the parallel result of Cassidy et al. (J Aust Math Soc 38:287-329, 1985), linking factorization systems and reflective subcategories. Â© 2008 Springer Science+Business Media B.V.
(2011). Weak reflections and weak factorization systems. Applied Categorical Structures, 19(1), 9–38.
"Weak reflections and weak factorization systems." Applied Categorical Structures, vol. 19,no. 1, 2011, pp. 9–38.