  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.
