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Journal Articles Journal of Pure and Applied Algebra Year : 2022

Coherent confluence modulo relations and double groupoids

Benjamin Dupont
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Philippe Malbos

Abstract

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.
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Dates and versions

hal-01898868 , version 1 (19-10-2018)
hal-01898868 , version 2 (12-02-2019)
hal-01898868 , version 3 (08-07-2023)

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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⟩
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