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.2017.12
URN: urn:nbn:de:0030-drops-80334
URL: https://drops.dagstuhl.de/opus/volltexte/2017/8033/
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Fong, Brendan ; Zanasi, Fabio

A Universal Construction for (Co)Relations

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LIPIcs-CALCO-2017-12.pdf (0.6 MB)


Abstract

Calculi of string diagrams are increasingly used to present the syntax and algebraic structure of various families of circuits, including signal flow graphs, electrical circuits and quantum processes. In many such approaches, the semantic interpretation for diagrams is given in terms of relations or corelations (generalised equivalence relations) of some kind. In this paper we show how semantic categories of both relations and corelations can be characterised as colimits of simpler categories. This modular perspective is important as it simplifies the task of giving a complete axiomatisation for semantic equivalence of string diagrams. Moreover, our general result unifies various theorems that are independently found in literature and are relevant for program semantics, quantum computation and control theory.

BibTeX - Entry

@InProceedings{fong_et_al:LIPIcs:2017:8033,
  author =	{Brendan Fong and Fabio Zanasi},
  title =	{{A Universal Construction for (Co)Relations}},
  booktitle =	{7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-033-0},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{72},
  editor =	{Filippo Bonchi and Barbara K{\"o}nig},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2017/8033},
  URN =		{urn:nbn:de:0030-drops-80334},
  doi =		{10.4230/LIPIcs.CALCO.2017.12},
  annote =	{Keywords: corelation, prop, string diagram}
}

Keywords: corelation, prop, string diagram
Collection: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Issue Date: 2017
Date of publication: 17.11.2017


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