Please use this identifier to cite or link to this item: http://hdl.handle.net/10316/43887
Title: Kan injectivity in order-enriched categories
Authors: Adamek, Jiri
Sousa, Lurdes
Velebil, Jiri
Issue Date: 2015
Publisher: Cambridge University Press
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.
Peer review: yes
URI: http://hdl.handle.net/10316/43887
DOI: 10.1017/S0960129514000024
Publisher Version: https://doi.org/10.1017/S0960129514000024
Appears in Collections:I&D CMUC - Artigos em Revistas Internacionais

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