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Lax orthogonal factorisations in ordered structures
Theory and applications of categories, Tome 35 (2020), pp. 1379-1423 Cet article a éte moissonné depuis la source Theory and Applications of Categories website

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We give an account of lax orthogonal factorisation systems on order-enriched categories. Among them, we define and characterise the KZ-reflective ones, in a way that mirrors the characterisation of reflective orthogonal factorisation systems. We use simple monads to construct lax orthogonal factorisation systems, such as one on the category of T_0 topological spaces closely related to continuous lattices.

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Classification : Primary 18D05, 18A32. Secondary 55U35
Keywords: lax orthogonal factorization system, lax idempotent monad, order-enriched category, weak factorization system, reflective factorization system, continuous lattice 
@article{TAC_2020_35_a35,
     author = {Maria Manuel Clementino and Ignacio L\'opez Franco},
     title = {Lax orthogonal factorisations in ordered structures},
     journal = {Theory and applications of categories},
     pages = {1379--1423},
     year = {2020},
     volume = {35},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2020_35_a35/}
}
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Maria Manuel Clementino; Ignacio López Franco. Lax orthogonal factorisations in ordered structures. Theory and applications of categories, Tome 35 (2020), pp. 1379-1423. http://geodesic.mathdoc.fr/item/TAC_2020_35_a35/