Wilson, P;
Ghica, D;
Zanasi, F;
(2023)
String Diagrams for Non-Strict Monoidal Categories.
In:
31st EACSL Annual Conference on Computer Science Logic (CSL 2023).
(pp. 37:1-37:19).
Schloss Dagstuhl -- Leibniz-Zentrum für Informatik: Dagstuhl, Germany.
Preview |
PDF
LIPIcs-CSL-2023-37.pdf - Published Version Download (861kB) | Preview |
Abstract
Whereas string diagrams for strict monoidal categories are well understood, and have found application in several fields of Computer Science, graphical formalisms for non-strict monoidal categories are far less studied. In this paper, we provide a presentation by generators and relations of string diagrams for non-strict monoidal categories, and show how this construction can handle applications in domains such as digital circuits and programming languages. We prove the correctness of our construction, which yields a novel proof of Mac Lane’s strictness theorem. This in turn leads to an elementary graphical proof of Mac Lane’s coherence theorem, and in particular allows for the inductive construction of the canonical isomorphisms in a monoidal category.
| Type: | Proceedings paper |
|---|---|
| Title: | String Diagrams for Non-Strict Monoidal Categories |
| Event: | 31st EACSL Annual Conference on Computer Science Logic (CSL 2023) |
| ISBN-13: | 9783959772648 |
| Open access status: | An open access version is available from UCL Discovery |
| DOI: | 10.4230/LIPIcs.CSL.2023.37 |
| Publisher version: | https://doi.org/10.4230/LIPIcs.CSL.2023.37 |
| Language: | English |
| Additional information: | © Paul Wilson, Dan Ghica, and Fabio Zanasi; licensed under Creative Commons License CC-BY 4.0 |
| Keywords: | String Diagrams, Strictness, Coherence |
| 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/10166259 |
Archive Staff Only
 |
View Item |
