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oai:drops-oai.dagstuhl.de:8033 2024-03-06T10:39:38Z ddc:004 open_access

A Universal Construction for (Co)Relations Fong, Brendan Zanasi, Fabio corelation prop string diagram 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. Schloss Dagstuhl – Leibniz-Zentrum für Informatik Brendan Fong and Fabio Zanasi 2017 Is Part Of LIPIcs, Volume 72, 7th Conference on Algebra and Coalgebra in Computer Science (CALCO 2017) InProceedings Text doc-type:ResearchArticle publishedVersion application/pdf doi:10.4230/LIPIcs.CALCO.2017.12 urn:nbn:de:0030-drops-80334 https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CALCO.2017.12 eng https://creativecommons.org/licenses/by/3.0/legalcode