Dan Marsden: "Custom hypergraph categories via generalized relations"

Talk given as part of Categories Logic and Physics Scotland: http://conferences.inf.ed.ac.uk/clapscotland. Compact closed and hypergraph categories have become standard settings for work in categorical quantum mechanics, linguistics and general process theories. More recently, our group in Oxford has been looking at further applications in areas such as cognition. With each new application area, there is a need to identify a suitable category modelling thppe phenomena under consideration. In this talk we will describe a framework derived from generalized notions of relations, in which we can construct hypergraph categories which can capture features such as convexity, proof relevance, metrics and semantics varying with time or context. The framework is parameterized along 4 natural axes of variation, allowing users to flexibly configure hypergraph categories to their application needs.