String Diagrams for Premonoidal Categories (Román, 2023)

Abstract

Premonoidal and Freyd categories are both generalized by non-cartesian Freyd categories: effectful categories. We construct string diagrams for effectful categories in terms of the string diagrams for a monoidal category with a freely added object.

• ArXiv preprint.
• This paper is an extended journal version of the first part of Promonads and String Diagrams for Effectful Categories (Roman, 2022), presented at ACT 2022.

@article{rs:stringsPremonoidal,
    title      = {String Diagrams for Premonoidal Categories},
    author     = {Mario Román and Paweł Sobociński},
    url        = {https://lmcs.episciences.org/13384},
    doi        = {10.46298/lmcs-21(2:9)2025},
    journal    = {Logical Methods in Computer Science},
    issn       = {1860-5974},
    volume     = {Volume 21, Issue 2},
    eid        = 9,
    year       = {2025},
    month      = {Apr},
    keywords   = {Mathematics - Category Theory, 18M30},
}