Promonads and String Diagrams for Effectful Categories (Román, 2022)

Last updated Oct 14, 2024

Effectful program in string diagrammatic notation and arrow-do notation.

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. We show that effectful categories are pseudomonoids in a monoidal bicategory of promonads with a suitable tensor product.

# How to cite

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@inproceedings{effectful22,
  author    = {Mario Rom{\'{a}}n},
  title     = {Promonads and String Diagrams for Effectful Categories},
  booktitle = {{ACT} '22: Applied Category Theory, Glasgow, United Kingdom, 18 - 22 July, 2022},
  volume    = {abs/2205.07664},
  year      = {2022},
  url       = {https://doi.org/10.48550/arXiv.2205.07664},
  doi       = {10.48550/arXiv.2205.07664},
  eprinttype = {arXiv},
  eprint    = {2205.07664},
  timestamp = {Wed, 18 May 2022 10:38:32 +0200},
  biburl    = {https://dblp.org/rec/journals/corr/abs-2205-07664.bib},
  bibsource = {dblp computer science bibliography, https://dblp.org}
}

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