Duality and canonical extensions for stably compact spaces

TL;DR

This paper develops a canonical extension framework for strong proximity lattices to provide an algebraic, point-free duality theory for stably compact spaces, allowing distinct pi- and sigma-extensions for objects and morphisms.

Contribution

It introduces a canonical extension for strong proximity lattices, enabling a finitary duality for stably compact spaces with separate pi- and sigma-extensions.

Findings

Constructed a canonical extension for strong proximity lattices.

Provided an algebraic, point-free duality for stably compact spaces.

Allowed objects and morphisms to have distinct pi- and sigma-extensions.

Abstract

We construct a canonical extension for strong proximity lattices in order to give an algebraic, point-free description of a finitary duality for stably compact spaces. In this setting not only morphisms, but also objects may have distinct pi- and sigma-extensions.