## 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.

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