All hypergraph categories are decorated corelation categories

Brendan Fong – 14 December 2016

Hypergraph categories are symmetric monoidal categories in which every object is equipped with a special commutative Frobenius monoid (with a coherence condition). Morphisms in a hypergraph category can hence be represented by string diagrams in which strings can branch and split: diagrams (hypergraphs) that are reminiscent of electrical circuit diagrams. As such they provide a framework for formalising the syntax and semantics of circuit-type diagrammatic languages.

In this talk I will introduce decorated corelations as a tool for building hypergraph categories and hypergraph functors. We shall see that all hypergraph categories and hypergraph functors can be constructed in this way.