Hypergraph categories

Custom Hypergraph Categories via Generalized Relations

Process theories combine a graphical language for compositional reasoning with an underlying categorical semantics. They have been successfully applied to fields such as quantum computation, natural language processing, linear dynamical systems and network theory. When investigating a new application, the question arises of how to identify a suitable process theoretic model. We present a concep...

Hypergraph Rewriting

In their pioneering paper [KB70], Knuth and Bendix showed that con uence (or, equivalently, the Church-Rosser property) is decidable for terminating term rewriting systems. It su ces to compute all critical pairs t s ! u of rewrite steps in which s is the superposition of the left-hand sides of two rules, and to check whether t and u reduce to a common term. This procedure is justi ed by the so...

Hypergraph Codes

Hypergraph Games

The above is called the “strong” version of the game. In the “weak” version, also called “maker-breaker”, the second player’s aim is not to occupy a winning set but just to prevent the first player from doing so. The interest is both for general theorems about games and also in particular games of interest, like the Hales-Jewett game (multi-dimensional noughts & crosses). Roughly speaking, a fa...

OPERADIC CATEGORIES, A∞-CATEGORIES AND n-CATEGORIES

When I offered to talk here, I asked myself if I had something suitable for a nice short 20 minute talk, and sent in an abstract about “cores of spaces and spectra”. However, since I have been given 50 minutes, I have decided to scrap that for something a little more substantial. It is brand new. I assume that I am among friends and that you won’t mind if some of what I say turns out to be nons...