REVIEW 1 cited by
Rewriting in Free Hypergraph Categories
Not yet reviewed by Pith; the record is open.
This paper has not been read by Pith yet. Machine review is queued; the pith claim, tier, and objections will appear here once it completes.
SPECIMEN: schema-true, not a live event
T0 review · schema-true
One-sentence machine reading of the paper's core claim.
pith:XXXXXXXX · record.json · timestamp
read the original 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.
Forward citations
Cited by 1 Pith paper
-
Guarded Realization Semantics: Occurrence-Sensitive Certificates and Behavior-Dependent Lower Bounds
Under stated guards, every realization satisfies Q(O(Err(r))) ≤ A(Err(r)) ≤ U(r), with U from occurrence-sensitive certificates and Q from behavior-fiber or quotient-norm reflection.
Discussion (0). Continue with ORCID to comment.