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 N-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].
The dual of compact ordered spaces is a variety / M. Abbadini. - In: THEORY AND APPLICATIONS OF CATEGORIES. - ISSN 1201-561X. - 34:(2019), pp. 1401-1439.
The dual of compact ordered spaces is a variety
M. Abbadini
2019
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 N-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].
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