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DOI: 10.4230/LIPIcs.CALCO.2025.11

Tape Diagrams for Monoidal Monads

Authors: Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio, and Elena Di Lavore

Published in: LIPIcs, Volume 342, 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)

Abstract

Tape diagrams provide a graphical representation for arrows of rig categories, namely categories equipped with two monoidal structures, ⊕ and ⊗, where ⊗ distributes over ⊕. However, their applicability is limited to categories where ⊕ is a biproduct, i.e., both a categorical product and a coproduct. In this work, we extend tape diagrams to deal with Kleisli categories of symmetric monoidal monads, presented by algebraic theories.

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Filippo Bonchi, Cipriano Junior Cioffo, Alessandro Di Giorgio, and Elena Di Lavore. Tape Diagrams for Monoidal Monads. In 11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 342, pp. 11:1-11:24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{bonchi_et_al:LIPIcs.CALCO.2025.11,
  author =	{Bonchi, Filippo and Cioffo, Cipriano Junior and Di Giorgio, Alessandro and Di Lavore, Elena},
  title =	{{Tape Diagrams for Monoidal Monads}},
  booktitle =	{11th Conference on Algebra and Coalgebra in Computer Science (CALCO 2025)},
  pages =	{11:1--11:24},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-383-6},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{342},
  editor =	{C\^{i}rstea, Corina and Knapp, Alexander},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2025.11},
  URN =		{urn:nbn:de:0030-drops-235703},
  doi =		{10.4230/LIPIcs.CALCO.2025.11},
  annote =	{Keywords: rig categories, string diagrams, monads, probabilistic control}
}

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Tape Diagrams for Monoidal Monads

Abstract

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