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 ℵ1. 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].
| Original language | English |
|---|---|
| Pages (from-to) | 1401-1439 |
| Journal | Theory and Applications of Categories |
| Volume | 34 |
| Issue number | 44 |
| Publication status | Published - 2019 |
Keywords
- compact ordered space
- variety
- duality
- axiomatizability