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

Category Theory