Giacomo Cozzi: Classifying Locales: Connecting topology, category theory and logic

Abstract

Locales are mathematical objects that both generalize topological spaces (and are the foundation of "pointless topology"), and also classify certain logical theories, the so called "geometric theories". This talk will be a gentle introduction to locales from both these perspectives, and perhaps at the same time a fresh insight into topology and logic from the perspective of locales. A listener familiar with category theory will find a third connection. We will sketch a proof of the classification theorem connecting the two areas, and doing so get a glimpse into an idea behind "topos theory". It is interesting but not necessary to have some previous knowledge about topology, logic or category when following the talk.