License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CALCO.2019.18
URN: urn:nbn:de:0030-drops-114466
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2019/11446/
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Balco, Samuel ; Kurz, Alexander

Nominal String Diagrams

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LIPIcs-CALCO-2019-18.pdf (8 MB)

Abstract

We introduce nominal string diagrams as string diagrams internal in the category of nominal sets. This requires us to take nominal sets as a monoidal category, not with the cartesian product, but with the separated product. To this end, we develop the beginnings of a theory of monoidal categories internal in a symmetric monoidal category. As an instance, we obtain a notion of a nominal PROP as a PROP internal in nominal sets. A 2-dimensional calculus of simultaneous substitutions is an application.

BibTeX - Entry

@InProceedings{balco_et_al:LIPIcs:2019:11446,
  author =	{Samuel Balco and Alexander Kurz},
  title =	{{Nominal String Diagrams}},
  booktitle =	{8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)},
  pages =	{18:1--18:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-120-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{139},
  editor =	{Markus Roggenbach and Ana Sokolova},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2019/11446},
  URN =		{urn:nbn:de:0030-drops-114466},
  doi =		{10.4230/LIPIcs.CALCO.2019.18},
  annote =	{Keywords: string diagrams, nominal sets, separated product, simultaneous substitutions, internal category, monoidal category, internal monoidal categories, PRO}
}

Keywords: string diagrams, nominal sets, separated product, simultaneous substitutions, internal category, monoidal category, internal monoidal categories, PRO
Collection: 8th Conference on Algebra and Coalgebra in Computer Science (CALCO 2019)
Issue Date: 2019
Date of publication: 25.11.2019

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