Towards 3-Dimensional Rewriting Theory

Understand

String rewriting systems have proved very useful to study monoids.

• In good cases, they give finite presentations of monoids, allowing computations on those and their manipulation by a computer.
• Even better, when the presentation is confluent and terminating, they provide one with a notion of canonical representative of the elements of the presented monoid.
• Polygraphs are a higher-dimensional generalization of this notion of presentation, from the setting of monoids to the much more general setting of n-categories.