Paul Wilson ; Dan Ghica ; Fabio Zanasi - String diagrams for Strictification and Coherence

lmcs:13982 - Logical Methods in Computer Science, October 29, 2024, Volume 20, Issue 4 - https://doi.org/10.46298/lmcs-20(4:8)2024
String diagrams for Strictification and CoherenceArticle

Authors: Paul Wilson ; Dan Ghica ; Fabio Zanasi

    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.


    Volume: Volume 20, Issue 4
    Published on: October 29, 2024
    Accepted on: July 26, 2024
    Submitted on: July 26, 2024
    Keywords: Mathematics - Category Theory

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