A Constructive Proof of Coherence for Symmetric Monoidal Categories Using Rewriting
Abstract
A symmetric monoidal category is a category equipped with an associative and commutative (binary) product and an object which is the unit for the product. In fact, those properties only hold up to natural isomorphisms which satisfy some coherence conditions. The coherence theorem asserts the commutativity of all linear diagrams involving the left and right unitors, the associator and the braiding. We prove the coherence for symmetric monoidal categories using a homotopical method based on rewriting. For that scope, we detail the con vergence proof of Lafont's string diagram rewriting system which presents the isomorphisms of these theories.
Cite
@article{arxiv.1606.01722,
title = {A Constructive Proof of Coherence for Symmetric Monoidal Categories Using Rewriting},
author = {Matteo Acclavio},
journal= {arXiv preprint arXiv:1606.01722},
year = {2017}
}
Comments
The classification and solutions of rewriting system critical pairs have been corrected> The proof of the main theorems have been detailed and comparison with previous and related work added