caa a22 4500 44537862X CHVBK 20180317143010.0 cr unu---uuuuu 170323e20110201xx s 000 0 eng 10.1007/s10485-008-9164-1 doi (NATIONALLICENCE)springer-10.1007/s10485-008-9164-1 Hébert Michel Department of Mathematics, The American University in Cairo, Box 2511, Cairo, Egypt aut Weak Reflections and Weak Factorization Systems [Elektronische Daten] [Michel Hébert] We describe a one-to-one correspondence between saturated weak factorization systems and weak reflections in categories $\mathcal{C}$ with finite products. This actually extends to an adjunction between the category of natural weak factorization systems on $\mathcal{C}$ (in the sense of Grandis and Tholen, Arch Math 42:397-408, 2006, and Garner, arXiv preprint, 2007) and the category of monads on $\mathcal{C}$. Explicit comparisons are made with the parallel result of Cassidy etal. (J Aust Math Soc 38:287-329, 1985), linking factorization systems and reflective subcategories. Springer Science+Business Media B.V., 2008 Factorization system nationallicence Weak factorization system nationallicence Reflection nationallicence Weak reflection nationallicence Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 9-38 0927-2852 19:1<9 2011 19 10485 https://doi.org/10.1007/s10485-008-9164-1 text/html Onlinezugriff via DOI 1 research-article jats NATIONALLICENCE 856 40 https://doi.org/10.1007/s10485-008-9164-1 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Hébert Michel Department of Mathematics, The American University in Cairo, Box 2511, Cairo, Egypt aut NATIONALLICENCE 773 0- Applied Categorical Structures Springer Netherlands 19/1(2011-02-01), 9-38 0927-2852 19:1<9 2011 19 10485 Metadata rights reserved Springer special CC-BY-NC licence nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-springer