Geodesic
The dual of compact ordered spaces is a variety
Theory and applications of categories, Tome 34 (2019), pp. 1401-1439

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In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact ordered spaces and monotone continuous maps is a quasi-variety -not finitary, but bounded by $\aleph_1$. An open question was: is it also a variety? We show that the answer is affirmative. We describe the variety by means of a set of finitary operations, together with an operation of countably infinite arity, and equational axioms. The dual equivalence is induced by the dualizing object [0,1].

Publié le :
Classification : Primary: 03C05. Secondary: 08A65, 18B30, 18C10, 54A05, 54F05
Keywords: compact ordered space, variety, duality, axiomatizability 
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     author = {Marco Abbadini},
     title = {The dual of compact ordered spaces is a variety},
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     pages = {1401--1439},
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     volume = {34},
     year = {2019},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/TAC_2019_34_a43/}
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Marco Abbadini. The dual of compact ordered spaces is a variety. Theory and applications of categories, Tome 34 (2019), pp. 1401-1439. http://geodesic.mathdoc.fr/item/TAC_2019_34_a43/