Coherence in monoidal track categories

Details Coherence in monoidal track categories Coherence in monoidal track categories

2010-04-07

arxiv.org/abs/1004.1055v2

Mathematics

Category Theory

32 pages

Scientific paper

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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