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  • 标题:Coherence of Gray Categories via Rewriting
  • 作者:Simon Forest ; Samuel Mimram
  • 期刊名称:LIPIcs : Leibniz International Proceedings in Informatics
  • 电子版ISSN:1868-8969
  • 出版年度:2018
  • 卷号:108
  • 页码:15:1-15:16
  • DOI:10.4230/LIPIcs.FSCD.2018.15
  • 出版社:Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
  • 摘要:Over the recent years, the theory of rewriting has been extended in order to provide systematic techniques to show coherence results for strict higher categories. Here, we investigate a further generalization to low-dimensional weak categories, and consider in details the first non-trivial case: presentations of tricategories. By a general result, those are equivalent to the stricter Gray categories, for which we introduce a notion of rewriting system, as well as associated tools: critical pairs, termination orders, etc. We show that a finite rewriting system admits a finite number of critical pairs and, as a variant of Newman's lemma in our context, that a convergent rewriting system is coherent, meaning that two parallel 3-cells are necessarily equal. This is illustrated on rewriting systems corresponding to various well-known structures in the context of Gray categories (monoids, adjunctions, Frobenius monoids). Finally, we discuss generalizations in arbitrary dimension.
  • 关键词:rewriting; coherence; Gray category; polygraph; pseudomonoid; precategory
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