Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Kan injectivity in order-enriched categories   Continuous lattices were characterised by Martin Escardo 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. 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 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-Zoeberlein monad. However, this
does not generalise to proper classes: we present a class of continuous
mappings in Top_0 for which Kan-injectivity does not yield a monadic category.

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The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
31
The categories of this paper are: ao-sci
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The categories of this paper are: alg-geom
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The categories of this paper are: quant-ph
5
The categories of this paper are: gr-qc
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The categories of this paper are: nlin
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The categories of this paper are: physics
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The categories of this paper are: q-fin
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The categories of this paper are: patt-sol
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The categories of this paper are: bayes-an
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The categories of this paper are: stat
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: chem-ph
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The categories of this paper are: plasm-ph