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Universal Constructions for (Co)Relations: categories, monoidal categories, and props

Fong, B; Zanasi, F; (2018) Universal Constructions for (Co)Relations: categories, monoidal categories, and props. Logical Methods in Computer Science , 14 (3) 10.23638/LMCS-14(3:14)2018. 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: Article
Title: Universal Constructions for (Co)Relations: categories, monoidal categories, and props
Open access status: An open access version is available from UCL Discovery
DOI: 10.23638/LMCS-14(3:14)2018
Publisher version: https://doi.org/10.23638/LMCS-14(3:14)2018
Language: English
Additional information: This is an Open Access article distributed under the terms of the Creative Commons Attribution License (https://creativecommons.org/licenses/by/4.0/).
UCL classification: UCL
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: https://discovery.ucl.ac.uk/id/eprint/10062963
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