Kan injectivity in order-enriched categories

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F15%3A00222681" target="_blank" >RIV/68407700:21230/15:00222681 - isvavai.cz</a>
Result on the web
<a href="http://dx.doi.org/10.1017/S0960129514000024" target="_blank" >http://dx.doi.org/10.1017/S0960129514000024</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1017/S0960129514000024" target="_blank" >10.1017/S0960129514000024</a>

Result language
angličtina
Original language name
Kan injectivity in order-enriched categories
Original language description
Continuous lattices were characterised by Martin Escardo 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. For every class H ofmorphisms, 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-Zoberlein 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.
Czech name
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Czech description
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Type
J<sub>x</sub> - Unclassified - Peer-reviewed scientific article (Jimp, Jsc and Jost)
CEP classification
BA - General mathematics
OECD FORD branch
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Project
<a href="/en/project/GAP202%2F11%2F1632" target="_blank" >GAP202/11/1632: Algebraic Methods in Proof Theory</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2015
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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