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- W3106368401 abstract "Continuous lattices were characterised by Martin Escardo as precisely the objects that are Kan-injective w.r.t. a certain class of morphisms. We study Kan-injectivity in general categories enriched in posets. For every class H of morphisms we study the subcategory of all objects Kan-injective w.r.t. H and all morphisms preserving Kan-extensions. For categories such as Top_0 and Pos we prove that whenever H is a set of morphisms, the above subcategory is monadic, and the monad it creates is a Kock-Zoeberlein monad. However, this does not generalise to proper classes: we present a class of continuous mappings in Top_0 for which Kan-injectivity does not yield a monadic category." @default.
- W3106368401 created "2020-11-23" @default.
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- W3106368401 date "2014-12-02" @default.
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- W3106368401 title "Kan injectivity in order-enriched categories" @default.
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- W3106368401 doi "https://doi.org/10.1017/s0960129514000024" @default.
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