Coherent confluence modulo relations and double groupoids

A coherent presentation of an n-category is a by generators, relations and among relations. Confluent terminating rewriting systems generate presentations, whose are defined confluence diagrams critical branchings. This article introduces procedure to compute presentations when the rewrite modulo set axioms. Our coherence results formulated using structure n-categories enriched in double groupoids, horizontal cells represent paths, vertical congruence generated axioms square induced modulo. We illustrate our constructions on commutation commutative monoids, isotopy pivotal monoidal categories, inverse groups.