preprint "Kan injectivity in order-enriched categories"

preprint "Kan injectivity in order-enriched categories"

[Jiri Adamek]

This is to announce a preprint

"Kan Injectivity in Order-Enriched Categories"
Jiri Adamek, Lurdes Sousa and Jiri Velebil

we have just uploaded to the arxiv

  	http://arxiv.org/abs/1311.1721

In an order-enriched category Escardo introduced Kan-injectivity of
an object X w.r.t. to a class H of moprhisms: this means that all
left Kan-extensions of morphisms with codomain X along all members
of H exist and the corresponding triangles commute.
We study the category LInj(H) of all Kan-injective objects and all
morphisms preserving left Kan-extensions (introduced by
Carvalho and Sousa). Example: for H consisting of all
subspace embeddings in the category Top_0 of T_0 spaces LInj(H) is the
category of continuous lattices and meet-preserving continuous functions.

Every KZ-monadic category has the form LInj(H). Conversely,
given  a set H of moprhisms in a "reasonable" order-enriched category,
then LInj(H) is proved to be KZ-monadic. However, a class of
continuous functions in Top_0 is presented for which LInj(H) is not
KZ-monadic.


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