TY - GEN EP - 37:19 A1 - Wilson, P A1 - Ghica, D A1 - Zanasi, F KW - String Diagrams KW - Strictness KW - Coherence TI - String Diagrams for Non-Strict Monoidal Categories CY - Dagstuhl, Germany Y1 - 2023/// SP - 37:1 T3 - Leibniz International Proceedings in Informatics (LIPIcs) SN - 1868-8969 N2 - 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. AV - public N1 - © Paul Wilson, Dan Ghica, and Fabio Zanasi; licensed under Creative Commons License CC-BY 4.0 ID - discovery10166259 UR - https://doi.org/10.4230/LIPIcs.CSL.2023.37 PB - Schloss Dagstuhl -- Leibniz-Zentrum für Informatik ER -