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Abstract: We introduce homotopical methods based on rewriting on higher-dimensionalcategories to prove coherence results in categories with an algebraicstructure. We express the coherence problem for symmetric monoidal categoriesas an asphericity problem for a track category and we use rewriting methods onpolygraphs to solve it. The setting is extended to more general coherenceproblems, seen as 3-dimensional word problems in a track category, includingthe case of braided monoidal categories.



Author: Yves Guiraud, Philippe Malbos

Source: https://arxiv.org/



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