  In this paper, we provide an alternative description of the duality result
for distributive lattices and coherent locales using ultraposet. In particular,
we show that there are fully faithful embeddings from the opposite of the
category of distributive lattices into the category of ultraposets with
ultrafunctors, and from the category of coherent locales into the category of
ultraposets with left ultrafunctors. We also define the notion of
zero-dimensional ultraposets, which characterises the essential image of these
embeddings.
