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.
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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 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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