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Hypergraphs for Compact Closed Categories

Authors Alessandro Di Giorgio , Callum Reader

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LIPIcs.MFCS.2026.50.pdf
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Subject Classification

ACM Subject Classification
  • Theory of computation → Rewrite systems
  • Theory of computation → Equational logic and rewriting
Keywords
  • rewriting
  • compact closed categories
  • string diagrams

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Abstract

In recent years a succession of papers have taken to representing string diagrams as hypergraphs, the advantage of which is that the structural equations of diagrams come for free from the hypergraph structure. This improves implementability and reduces the number of rewrites necessary for reasoning.
Notably, however, string diagrams for compact closed categories have escaped this treatment. In this paper we introduce a combinatorial interpretation of compact closed string diagrams, via the Int construction on hypergraphs for traced string diagrams. Using this interpretation, we characterise string diagram rewriting as a suitable adaptation of double-pushout rewriting.

Cite As Get BibTex

Alessandro Di Giorgio, Alessandro Di Giorgio, Callum Reader, and Callum Reader. Hypergraphs for Compact Closed Categories. In 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 386, pp. 50:1-50:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026) https://doi.org/10.4230/LIPIcs.MFCS.2026.50

Author Details

Alessandro Di Giorgio
  • Tallinn University of Technology, Estonia
Callum Reader
  • Tallinn University of Technology, Estonia

Funding

  • Di Giorgio, Alessandro: Supported by the European Union under Grant Agreement No. 101087529.
  • Reader, Callum: Supported by the Estonian Research Council via grant PRG3215.

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