# Diagrammatic sets between rewriting and topology

- 14:00 21st February 2020 ( week 5, Hilary Term 2020 )Lecture Theatre A

String rewriting, diagram rewriting, presentations of higher algebras,

and more can be put under the umbrella of “higher-dimensional

rewriting theory”. This field has some intriguing connections with

combinatorial topology, which are not fully realised when rewrite

systems are modelled, as commonly done, by strict higher categories. I

will show how following these connections can lead to an alternative

framework, immune from many technical problems: diagrammatic sets.

Then, I will discuss how one can build a model of weak higher

categories on top of diagrammatic sets, to function as a semantics of

higher-dimensional rewrite systems. This may provide a link between

mainstream models from categorical homotopy theory and diagrammatic

approaches popular in Oxford. This talk is based on arXiv:1909.07639.