The dual of compact ordered spaces is a variety

Abbadini, Marco
(2019) Theory and Applications of Categories — Vol. 34, p. 1401-1439 (2019)

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Abstract
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 N1. 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]. © Marco Abbadini, 2019.
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  • University of Milan

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Abbadini, M. (2019). The dual of compact ordered spaces is a variety. Theory and Applications of Categories, 34, 1401-1439. (Original work published 2019)