Coherent confluence modulo relations and double groupoids

Benjamin Dupont (1) , Philippe Malbos (1)

1 ICJ - Institut Camille Jordan

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 paper 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 confluences modulo. We illustrate our method on a diagrammatic presentation of a pivotal monoidal category modulo the isotopy relations.

Mots clés: Rewriting modulo; double categories; coherence of higher-dimensional 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. 2018. ⟨hal-01898868v1⟩