Coherence in monoidal track categories
Yves Guiraud, Philippe Malbos

TL;DR
This paper develops homotopical rewriting methods in higher-dimensional categories to solve coherence problems in monoidal and braided monoidal categories, framing them as asphericity and word problems.
Contribution
It introduces a novel homotopical approach using rewriting on polygraphs to establish coherence results in complex algebraic categories.
Findings
Reformulates coherence as an asphericity problem in track categories.
Extends methods to braided monoidal categories.
Provides a systematic rewriting framework for higher-dimensional coherence.
Abstract
We introduce homotopical methods based on rewriting on higher-dimensional categories to prove coherence results in categories with an algebraic structure. We express the coherence problem for (symmetric) monoidal categories as an asphericity problem for a track category and we use rewriting methods on polygraphs to solve it. The setting is extended to more general coherence problems, seen as 3-dimensional word problems in a track category, including the case of braided monoidal categories.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Algebraic structures and combinatorial models · Logic, programming, and type systems
