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Title: | Generating the algebraic theory of C(X): the case of partially ordered compact spaces |
Other Titles: | Generating the algebraic theory of $C(X)$: the case of partially ordered compact spaces |
Author: | Hofmann, Dirk Neves, Renato Nora, Pedro |
Keywords: | Ordered compact space Quasivariety Duality Coalgebra Vietoris functor Copresentable object Metrisable |
Issue Date: | 2018 |
Abstract: | It is known since the late 1960's that the dual of the category of compact Hausdorff spaces and continuous maps is a variety -- not finitary, but bounded by $\aleph_1$. In this note we show that the dual of the category of partially ordered compact spaces and monotone continuous maps is a $\aleph_1$-ary quasivariety, and describe partially its algebraic theory. Based on this description, we extend these results to categories of Vietoris coalgebras and homomorphisms. We also characterise the $\aleph_1$-copresentable partially ordered compact spaces. |
Peer review: | yes |
URI: | http://hdl.handle.net/10773/28976 |
ISSN: | 1201-561X |
Publisher Version: | http://www.tac.mta.ca/tac/volumes/33/12/33-12abs.html |
Appears in Collections: | CIDMA - Artigos AGG - Artigos DMat - Artigos |
Files in This Item:
File | Description | Size | Format | |
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coalgebras_duality_amsart.pdf | 465 kB | Adobe PDF | View/Open |
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