String Diagrams for Premonoidal Categories (Román, 2023)

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string-diagrams-for-premonoidal-categories

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.

string-diagrams-for-premonoidals

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@inproceedings{roman22:promonadseffectful,
  author       = {Mario Rom{\'{a}}n},
  editor       = {Jade Master and
                  Martha Lewis},
  title        = {Promonads and String Diagrams for Effectful Categories},
  booktitle    = {Proceedings Fifth International Conference on Applied Category Theory,
                  {ACT} 2022, Glasgow, United Kingdom, 18-22 July 2022},
  series       = {{EPTCS}},
  volume       = {380},
  pages        = {344--361},
  year         = {2022},
  url          = {https://doi.org/10.4204/EPTCS.380.20},
  doi          = {10.4204/EPTCS.380.20},
  timestamp    = {Fri, 11 Aug 2023 14:29:27 +0200},
  biburl       = {https://dblp.org/rec/journals/corr/abs-2205-07664.bib},
  bibsource    = {dblp computer science bibliography, https://dblp.org}
}