Rewriting in Free Hypergraph Categories

Fabio Zanasi
(University College London)

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.

In Timo Kehrer and Alice Miller: Proceedings Third Workshop on Graphs as Models (GaM 2017), Uppsala, Sweden, 23rd April 2017, Electronic Proceedings in Theoretical Computer Science 263, pp. 16–30.
Published: 22nd December 2017.

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