Centre for Mathematics, University of Coimbra

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Type:	Preprint
National /International:	International
Title:	Kan injectivity in order-enriched categories
Publication Date:	2013-11-13
Authors:	- Jirí Adámek - Lurdes Sousa - Jirí Velebil
Abstract:	Continuous lattices were characterised by Martín Escardó 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. An example: ω-CPO’s are precisely the posets that are Kan-injective w.r.t. the embeddings ω -> ω + 1 and 0 -> 1. 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 Top₀ 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-Zoberlein monad. However, this does not generalise to proper classes: we present a class of continuous mappings in Top₀ for which Kan-injectivity does not yield a monadic category.
Institution:	DMUC 13-52
Online version:	http://www.mat.uc.pt...prints/eng_2013.html
Download:	Not available