Realizability toposes, uniform preorders, and quantaloid enriched categories

Jonas Frey – 10 September 2014, 17 September 2014, 24 September 2014

I'll start my talk by recalling the construction and basic facts about realizability toposes over partial combinatory algebras (PCAs). Then I'll present generalizations of the notion of PCA leading to the concept of "uniform preorder". If time permits, I'll explain how uniform preorders can be viewed as categories enriched in a quantaloid of sets and families of relations, and how to characterize PCAs among uniform preorders.