Lax orthogonal factorisations in ordered structures
classification
🧮 math.CT
keywords
orthogonalfactorisationsystemsaccountcategoriescategorycharacterisationcharacterise
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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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