  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.
