Coherent confluence modulo relations and double groupoids

Benjamin Dupont (1) , Philippe Malbos (1)

1 AGL - Algèbre, géométrie, logique

A coherent presentation of an n-category is a presentation by generators, relations and relations among relations. Completions of presentations by rewriting systems give coherent presentations, whose relations among relations are generated by confluence diagrams induced by critical branchings. This article extends this construction to presentations by polygraphs defined modulo a set of relations. Our coherence results are formulated using the structure of n-category enriched in double groupoids, whose horizontal cells represent rewriting sequences, vertical cells represent the congruence generated by relations modulo and square cells represent coherence cells induced by confluence modulo. We illustrate these constructions for rewriting modulo commutation relations in monoids and isotopy relations in pivotal monoidal categories.

Mots clés: Rewriting modulo; coherence of higher-dimensional categories; coherence of higher categories; double categories

Domaines: Catégories et ensembles [math.CT]; Algorithme et structure de données [cs.DS]

Benjamin Dupont, Philippe Malbos. Coherent confluence modulo relations and double groupoids. Journal of Pure and Applied Algebra, 2022, 226 (10), pp.107037. ⟨10.1016/j.jpaa.2022.107037⟩. ⟨hal-01898868v3⟩