Please use this identifier to cite or link to this item:
https://hdl.handle.net/10316/43887
Title: | Kan injectivity in order-enriched categories | Authors: | Adamek, Jíri Sousa, Lurdes Velebil, Jirí |
Issue Date: | 2015 | Publisher: | Cambridge University Press | Project: | info:eu-repo/grantAgreement/FCT/COMPETE/132981/PT | Serial title, monograph or event: | Mathematical Structures in Computer Science | Volume: | 25 | Issue: | 01 | 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: | https://hdl.handle.net/10316/43887 | DOI: | 10.1017/S0960129514000024 10.1017/S0960129514000024 |
Rights: | embargoedAccess |
Appears in Collections: | I&D CMUC - Artigos em Revistas Internacionais |
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kan_inj_2013_11_23.pdf | 237.84 kB | Adobe PDF | View/Open |
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