Rewriting in Free Hypergraph Categories release_ivhqmh75lvhdhdimyo5sl6caga

by Fabio Zanasi

Released as a article .

2018  

Abstract

We study rewriting for equational theories in the context of symmetric monoidal categories where there is a separable Frobenius monoid on each object. These categories, also called hypergraph categories, are increasingly relevant: Frobenius structures recently appeared in cross-disciplinary applications, including the study of quantum processes, dynamical systems and natural language processing. In this work we give a combinatorial characterisation of arrows of a free hypergraph category as cospans of labelled hypergraphs and establish a precise correspondence between rewriting modulo Frobenius structure on the one hand and double-pushout rewriting of hypergraphs on the other. This interpretation allows to use results on hypergraphs to ensure decidability of confluence for rewriting in a free hypergraph category. Our results generalise previous approaches where only categories generated by a single object (props) were considered.
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Type  article
Stage   accepted
Date   2018-01-03
Version   v2
Language   en ?
arXiv  1712.09495v2
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