The dual of compact partially ordered spaces is a variety

Marco Abbadini

Published 2019-02-19Version 1

In a recent paper (2018), D. Hofmann, R. Neves and P. Nora proved that the dual of the category of compact partially 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 finite set of finitary operations, together with a single operation of countably infinite arity, and equational axioms. The dual equivalence is induced by the dualizing object [0,1].