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Coherence in monoidal track categories

Published online by Cambridge University Press:  30 October 2012

YVES GUIRAUD  and
PHILIPPE MALBOS
YVES GUIRAUD
Affiliation:
Institut Camille Jordan, INRIA, Université Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
PHILIPPE MALBOS
Affiliation:
Institut Camille Jordan, INRIA, Université Lyon 1, 43 boulevard du 11 novembre 1918, 69622 Villeurbanne cedex, France
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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 use rewriting methods on polygraphs to solve it. The setting is extended to more general coherence problems, viewed as 3-dimensional word problems in a track category, including the case of braided monoidal categories.

Type
Paper
Information
Mathematical Structures in Computer Science , Volume 22 , Issue 6: CAMCAD '09 Commutativity of Algebraic Diagrams , December 2012 , pp. 931 - 969
Copyright
Copyright © Cambridge University Press 2012

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