Finite groupoids, acyclicity & symmetries

Martin Otto

Groupoids (rather than groups) and their Cayley graphs can support generic constructions of finite hypergraphs that realise a prescribed local overlap pattern, satisfy certain acyclicity conditions, and respect the symmetries of the specification. Such constructions can be used to obtain hypergraph covers, models for GF, and solutions to extension tasks for partial isomorphisms, among other conceivable applications.