{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,7,30]],"date-time":"2025-07-30T16:53:26Z","timestamp":1753894406486,"version":"3.41.2"},"reference-count":0,"publisher":"Centre pour la Communication Scientifique Directe (CCSD)","content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":[],"abstract":"<jats:p>Whereas string diagrams for strict monoidal categories are well understood,\nand have found application in several fields of Computer Science, graphical\nformalisms for non-strict monoidal categories are far less studied. In this\npaper, we provide a presentation by generators and relations of string diagrams\nfor non-strict monoidal categories, and show how this construction can handle\napplications in domains such as digital circuits and programming languages. We\nprove the correctness of our construction, which yields a novel proof of Mac\nLane's strictness theorem. This in turn leads to an elementary graphical proof\nof Mac Lane's coherence theorem, and in particular allows for the inductive\nconstruction of the canonical isomorphisms in a monoidal category.<\/jats:p>","DOI":"10.46298\/lmcs-20(4:8)2024","type":"journal-article","created":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T09:40:10Z","timestamp":1730194810000},"source":"Crossref","is-referenced-by-count":0,"title":["String diagrams for Strictification and Coherence"],"prefix":"10.46298","volume":"Volume 20, Issue 4","author":[{"given":"Paul","family":"Wilson","sequence":"first","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Dan","family":"Ghica","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Fabio","family":"Zanasi","sequence":"additional","affiliation":[],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"25203","published-online":{"date-parts":[[2024,10,29]]},"container-title":["Logical Methods in Computer Science"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/lmcs.episciences.org\/14637\/pdf","content-type":"application\/pdf","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/lmcs.episciences.org\/14637\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2024,10,29]],"date-time":"2024-10-29T09:40:10Z","timestamp":1730194810000},"score":1,"resource":{"primary":{"URL":"https:\/\/lmcs.episciences.org\/13982"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2024,10,29]]},"references-count":0,"URL":"https:\/\/doi.org\/10.46298\/lmcs-20(4:8)2024","relation":{"has-preprint":[{"id-type":"arxiv","id":"2201.11738v3","asserted-by":"subject"}],"is-same-as":[{"id-type":"arxiv","id":"2201.11738","asserted-by":"subject"},{"id-type":"doi","id":"10.48550\/arXiv.2201.11738","asserted-by":"subject"}]},"ISSN":["1860-5974"],"issn-type":[{"type":"electronic","value":"1860-5974"}],"subject":[],"published":{"date-parts":[[2024,10,29]]},"article-number":"13982"}}