Coherence of quasi-terminating decreasing 2-polygraphs
Résumé
Craig Squier introduced a combinatorial method based on rewriting in order to describe relations amongst relations for presentations of monoids. From a rewriting system he constructed a 2-dimensional combinatorial complex whose 2-cells are generated by relations induced by the rewriting rules. When the rewriting system is confluent and terminating, he characterized the homotopy of this complex in term of confluence diagrams induced by the critical branchings. In this work, we weaken the termination hypothesis and we prove such a result for quasi-terminating decreasing rewriting systems.