What is the relation between the Synthetic Stone Duality and ASD?

[anshwad10]

I noticed that you use the term overtly discrete spaces which was introduced by Paul Taylor for Abstract Stone Duality. How are these uses of the term related to how it is used in ASD? Is there a model of ASD in Synthetic Stone Duality, or vice versa?

[felixwellen]

I don't remember the setup of ASD, but we showed once, that in SSD, you can prove the axioms of another approach to the topic by Reid Barton and Johann Commelin, which was inspired by ASD. They also used the notion of overt discreteness.
Details should be here:
https://felix-cherubini.de/condensed-cohomology-article.pdf