Coherence in monoidal track categories

Yves Guiraud (1) , Philippe Malbos (2)

1 PAREO - Formal islands: foundations and applications
2 ICJ - Institut Camille Jordan

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 use rewriting methods on polygraphs to solve it. The setting is generalized to more general coherence problems, seen as 3-dimensional word problems in a track category. We prove general results that, in the case of braided monoidal categories, yield the coherence theorem for braided monoidal categories.

Mots clés: coherence; monoidal category; higher-dimensional track category; rewriting; polygraph

Domaines: Catégories et ensembles [math.CT]

Yves Guiraud, Philippe Malbos. Coherence in monoidal track categories. 2010. ⟨hal-00470795v1⟩