Title: Kan injectivity in order-enriched categories
Authors: Adamek, Jiri 
Sousa, Lurdes 
Velebil, Jiri 
Issue Date: 2015
Publisher: Cambridge University Press
Project: info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT 
Abstract: 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 in posets. As an example, ω-CPO's are precisely the posets that are Kan-injective with respect to the embeddings ω ↪ ω + 1 and 0 ↪ 1. For every class H of morphisms, we study the subcategory of all objects that are Kan-injective with respect to 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–Zöberlein monad. However, this does not generalise to proper classes, and we present a class of continuous mappings in Top_0 for which Kan-injectivity does not yield a monadic category.
URI: http://hdl.handle.net/10316/43887
Other Identifiers: 10.1017/S0960129514000024
DOI: 10.1017/S0960129514000024
Rights: embargoedAccess
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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