The dual of compact ordered spaces is a variety
Marco Abbadini · Theory and applications of categories · 2019
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 ℵ 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].