文章基本信息

标题：A Universal Construction for (Co)Relations
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作者：Brendan Fong ; Fabio Zanasi
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：72
页码：12:1-12:16
DOI：10.4230/LIPIcs.CALCO.2017.12
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：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.
关键词：corelation; prop; string diagram