Kan injectivity in order-enriched categories

• DOI: 10.1017/s0960129514000024
• Publication Date: 2014-12-02T14:43:56Z
• Authors: JIŘÍ ADÁMEK; LURDES SOUSA; JIŘÍ VELEBIL
• Keywords: Morphism; Monad (category theory); Subcategory; Monomorphism

Continuous lattices were characterised by Martín Escardó as precisely those objects that are Kan-injective with respect to a certain class of morphisms. In this paper we study Kan-injectivity in general categories enriched posets. As an example, ω-CPO's the posets embeddings ω ↪ + 1 and 0 1. For every $\mathcal{H}$ morphisms, subcategory all morphisms preserving Kan extensions. such Top Pos , prove whenever is set above monadic, monad it creates Kock–Zöberlein monad. However, does not generalise proper classes, present continuous mappings for which yield monadic category.