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DOI: 10.4230/LIPIcs.MFCS.2026.50

Hypergraphs for Compact Closed Categories

Authors: Alessandro Di Giorgio and Callum Reader

Published in: LIPIcs, Volume 386, 51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)

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.

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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)

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@InProceedings{digiorgio_et_al:LIPIcs.MFCS.2026.50,
  author =	{Di Giorgio, Alessandro and Reader, Callum},
  title =	{{Hypergraphs for Compact Closed Categories}},
  booktitle =	{51st International Symposium on Mathematical Foundations of Computer Science (MFCS 2026)},
  pages =	{50:1--50:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-442-0},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{386},
  editor =	{Kouck\'{y}, Michal and Petrișan, Daniela},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2026.50},
  URN =		{urn:nbn:de:0030-drops-274318},
  doi =		{10.4230/LIPIcs.MFCS.2026.50},
  annote =	{Keywords: rewriting, compact closed categories, string diagrams}
}

Document

DOI: 10.4230/LIPIcs.CSL.2026.12

String Diagrams for Closed Symmetric Monoidal Categories

Authors: Callum Reader and Alessandro Di Giorgio

Published in: LIPIcs, Volume 363, 34th EACSL Annual Conference on Computer Science Logic (CSL 2026)

Abstract

We introduce a graphical language for closed symmetric monoidal categories based on an extension of string diagrams with special bracket wires representing internal homs. These bracket wires make the structure of the internal hom functor explicit, allowing standard morphism wires to interact with them through a well-defined set of graphical rules. We establish the soundness and completeness of the diagrammatic calculus, and illustrate its expressiveness through examples drawn from category theory, logic and programming language semantics.

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Callum Reader and Alessandro Di Giorgio. String Diagrams for Closed Symmetric Monoidal Categories. In 34th EACSL Annual Conference on Computer Science Logic (CSL 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 363, pp. 12:1-12:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

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@InProceedings{reader_et_al:LIPIcs.CSL.2026.12,
  author =	{Reader, Callum and Di Giorgio, Alessandro},
  title =	{{String Diagrams for Closed Symmetric Monoidal Categories}},
  booktitle =	{34th EACSL Annual Conference on Computer Science Logic (CSL 2026)},
  pages =	{12:1--12:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-411-6},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{363},
  editor =	{Guerrini, Stefano and K\"{o}nig, Barbara},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2026.12},
  URN =		{urn:nbn:de:0030-drops-254369},
  doi =		{10.4230/LIPIcs.CSL.2026.12},
  annote =	{Keywords: diagrammatic languages, logic, lambda calculi}
}

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Documents authored by Reader, Callum

Hypergraphs for Compact Closed Categories

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String Diagrams for Closed Symmetric Monoidal Categories

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