Coherence in monoidal track categories

Understand

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.