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A Universal Construction for (Co)Relations

Fong, B; Zanasi, F; (2017) A Universal Construction for (Co)Relations. In: Bonchi, F and König, B, (eds.) Proceedings of the 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017). Leibniz International Proceedings in Informatics: Dagstuhl, Germany. Green open access

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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.

Type: Proceedings paper
Title: A Universal Construction for (Co)Relations
Event: 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017)
Location: Ljubljana, Slovenia
Dates: 12 June 2017 - 16 June 2017
Open access status: An open access version is available from UCL Discovery
DOI: 10.4230/LIPIcs.CALCO.2017.12
Publisher version: http://dx.doi.org/10.4230/LIPIcs.CALCO.2017.12
Language: English
Additional information: Copyright © Brendan Fong and Fabio Zanasi; licensed under Creative Commons License CC-BY (http://creativecommons.org/licenses/by/3.0/).
Keywords: corelation, prop, string diagram
UCL classification: UCL > Provost and Vice Provost Offices
UCL > Provost and Vice Provost Offices > UCL BEAMS
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science
UCL > Provost and Vice Provost Offices > UCL BEAMS > Faculty of Engineering Science > Dept of Computer Science
URI: http://discovery.ucl.ac.uk/id/eprint/1561449
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