2021-11-24: Jonathan Gorard (University of Cambridge)

Tue, 14 Oct 2025 16:51:42 +0000

Jonathan Gorard (University of Cambridge)

Homotopic and Compositional Aspects of (Hyper)graph Rewriting and Fundamental Physics

Abstract

Graph grammars and double-pushout rewriting are pretty old news at this point. But the abstract rewriting systems produced by (hyper)graph grammars actually carry an extremely rich compositional and algebraic structure, many aspects of which have remained woefully under-investigated. We will show how causality relations in non-deterministic hypergraph rewriting systems can effectively be captured by means of a strict monoidal 2-category (a “multiway system”), and how higher homotopy types may consequently be constructed by adjoining appropriate sets of additional rewriting rules, with the n → ∞ limit of the resulting n-fold category yielding an ∞-groupoid (the classifying space of which forms an (∞,1)-topos). We will discuss how this general framework has been applied pragmatically in the design of efficient automated theorem-proving and diagrammatic reasoning software, before concluding with a more speculative discussion of the potential applicability of the overall formalism to the foundations of physics (especially categorical quantum mechanics and discrete quantum gravity).

This is joint with Xerxes Arsiwalla.

2021-11-24 15:00:00 UTC
Online