Errol Yuksel and Gabriel Saadia: Ionads: A categorification of topological spaces

Abstract

It is often stated that toposes are the categorification of topological spaces. However, it is more accurate to say that toposes are a categorification of locales, which are themselves a mild generalisation of topological spaces where one forgets about the points focus solely on the poset of opens.

In this expository talk we will go over the notion of ionad, introduced by Richard Garner (“Ionads” https://arxiv.org/abs/0912.1415v3) which bridges this gap.