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1 results

  • 11 - Termination of 3-Polygraphs

  • from Part III - Diagram Rewriting
  • Dimitri Ara, Aix-Marseille Université, Albert Burroni, Université Paris Cité, Yves Guiraud, Université Paris Cité, Philippe Malbos, Université Claude Bernard Lyon 1, François Métayer, Université Paris Cité, Samuel Mimram, École Polytechnique, Paris
  • Book:
    Polygraphs: From Rewriting to Higher Categories
    Published online:
    18 March 2025
    Print publication:
    03 April 2025, pp 237-248

  • Summary

    This chapter presents techniques for proving the termination of 3-polygraphs. A first method is based on a certain type of well-founded orders called reduction orders. Attention then turns to functorial interpretations: these amount to construct a functor from the underlying category to another category which already bears a reduction order. This covers quite a few useful examples. To address more complex cases, a powerful technique, due to Guiraud, is presented, based on the construction of a derivation from the polygraph. Here, termination is obtained by specifying quantities on 2-cells which decrease during rewriting, based on information propagated by the 2-cells themselves.